Applied Science, Faculty of
Mechanical Engineering, Department of
DSpace
UBCV
Ng, Denny
Master of Applied Science - MASc
University of British Columbia
The suitability of Sound Decay per Doubling of Distance (𝐷𝐿₂), as a universal room acoustics rating parameter was investigated. 𝐷𝐿₂ was combined with the Speech Transmission Index (𝑆𝑇𝐼) to rate acoustical room quality. This follows the methodology of ISO 3382-3, allowing evaluation of room quality using speech intelligibility as a foundation quantity. To prescribe rating criteria, all rooms where unamplified speech is present were postulated to be categorizable into one of three room types: Case 1 (intelligibility) rooms where intelligibility is required at all distances, Case 2 (distraction) rooms where distraction is permissible until a defined distance, or Case 3 (privacy) rooms where privacy is expected beyond a defined distance. For rating metrics, Case 1 used listening effort, Case 2 used loss of productivity, and Case 3 used percentage of speech intelligible. An idealized initial tool was developed which calculates 𝑆𝑇𝐼 at all points along a 𝐷𝐿₂ curve. The tool calculated 𝑆𝑇𝐼 based only on reverberant speech and was therefore applicable only to rooms where direct speech is impeded by obstacles. Assumptions used in the initial tool were checked using experimental data collected in 62 rooms of varying case classifications from 22 buildings. The data were used to evaluate the accuracy of regressions using sound pressure level measurements over a limited range of 1 – 16 m (𝐷𝐿2,𝑠,𝐴,1−16𝑚,), the octave band variation in 𝐷𝐿2, and the sound pressure level at 1 m from a sound source. The maximum regression error for 𝐷𝐿2,𝑠,𝐴,1−16𝑚, was 5.6 dB, and 2.5 dB on average. DL2 trends observed in the experimental data were then implemented in the DL2 tool and the STI calculation model was updated to include direct speech contributions. The updated tool was used to evaluate theoretical rooms for each case using the developed rating schemes. Room reverberation time (RT, 𝑇) and background noise levels (BNL, 𝐿𝑛) were modeled using values recommended in standards. Due to the variability of RT and BNL within rooms of similar types, standardized rating schemes based on 𝐷𝐿₂ were deemed unfeasible. However, 𝐷𝐿₂ and the tool developed provide valuable insight on how to optimize rooms acoustically.
Investigating Sound Decrement per Doubling of Distance as a Universal Room Acoustics Parameter by DENNY NG B.A.Sc. The University of British Columbia, 2014 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) February 2020 ©Denny Ng, 2020 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis entitled: Investigating Sound Decrement per Doubling of Distance as a Universal Room Acoustics Parameter Submitted by Denny Ng in partial fulfillment of the requirement for the degree of Master of Applied Science in Mechanical Engineering Examining Committee: Steve Rogak, Mechanical Engineering Supervisor Chris Waltham, Physics Supervisory Committee Member Shira Daltrop Supervisory Committee Member iii Abstract The suitability of Sound Decay per Doubling of Distance (𝐷𝐿2), as a universal room acoustics rating parameter was investigated. 𝐷𝐿2 was combined with the Speech Transmission Index (𝑆𝑇𝐼) to rate acoustical room quality. This follows the methodology of ISO 3382-3, allowing evaluation of room quality using speech intelligibility as a foundation quantity. To prescribe rating criteria, all rooms where unamplified speech is present were postulated to be categorizable into one of three room types: Case 1 (intelligibility) rooms where intelligibility is required at all distances, Case 2 (distraction) rooms where distraction is permissible until a defined distance, or Case 3 (privacy) rooms where privacy is expected beyond a defined distance. For rating metrics, Case 1 used listening effort, Case 2 used loss of productivity, and Case 3 used percentage of speech intelligible. An idealized initial tool was developed which calculates 𝑆𝑇𝐼 at all points along a 𝐷𝐿2 curve. The tool calculated 𝑆𝑇𝐼 based only on reverberant speech and was therefore applicable only to rooms where direct speech is impeded by obstacles. Assumptions used in the initial tool were checked using experimental data collected in 62 rooms of varying case classifications from 22 buildings. The data were used to evaluate the accuracy of regressions using sound pressure level measurements over a limited range of 1 – 16 m (𝐷𝐿2,𝑠,𝐴,1−16𝑚,), the octave band variation in 𝐷𝐿2, and the sound pressure level at 1 m from a sound source. The maximum regression error for 𝐷𝐿2,𝑠,𝐴,1−16𝑚, was 5.6 dB, and 2.5 dB on average. DL2 trends observed in the experimental data were then implemented in the DL2 tool and the STI calculation model was updated to include direct speech contributions. The updated tool was used to evaluate theoretical rooms for each case using the developed rating schemes. Room reverberation time (RT, 𝑇) and background noise levels (BNL, 𝐿𝑛) were modeled using values recommended in standards. Due to the variability of RT and BNL within rooms of similar types, standardized rating schemes based on 𝐷𝐿2 were deemed unfeasible. However, 𝐷𝐿2 and the tool developed provide valuable insight on how to optimize rooms acoustically. iv Lay Summary The rate that sound decreases with increasing distance from a sound source is proposed as a quantity for evaluating the acoustical quality of rooms. A model relating the rate of sound decay to the intelligibility of speech was implemented as a tool. Three room categories were hypothesized and a rating scheme for each category was developed. A literature review was conducted to find rating metrics that would be intuitive to lay users. The tool originally assumed perfect conditions and was verified using experimental data. Modifications were made according trends observed in the data to better approximate the real behavior of sound. The updated tool accepts reverberation time, background noise level, sound propagation and speech effort as inputs to produce charts relating intelligibility and distance. Due to variable room conditions, standardized ratings were not feasible and the tool is best suited for aiding design and remedial decisions. v Preface This dissertation includes a DL2 vs Distance model which uses a DL2 implementation scheme based on ISO 3382-3 “Acoustics – Measurement of room acoustic parameters – Part 3: Open plan offices”, which in turn is based on the publication “Determination of Acoustical Conditions in Open-Plan Offices: Proposala for New Measurement Method and Target Values” by Petra Virjonen, Jukka Keranen, and Valtteri Hongisto. Proposition of an alternative rating scheme as opposed to using the Speech Transmission Index (STI) is my original work. The ratings are based on existing research. The intelligibility case (Case 1, Chapter 2.2.1.1) and the privacy case (Case 3, Chapter 2.2.1.3) use data from J. Rennies and H. Schepker’s publication “Listening Effort and Speech Intelligibility in Listening Situations Affected by Noise and Reverberation”. Figure 2.5 of this thesis was taken directly from the aforementioned publication (Page 2647 of J. Acoust. Soc. Am., Vol. 136, No. 5, November 2014). The distraction case, (Case 2, Chapter 252.2.1.2) uses data from V. Hongisto’s publication “A model for Predicting the Effect of Speech of Varying Intelligibility on Work Performance”. Figure 2.6 of this thesis was taken directly from the aforementioned publication (Page 465 of Indoor Air, Vol. 15, 2006). The Speech Transmission Calculation schemes (reverberant speech calculation scheme and direct speech calculation scheme) were obtained from T. Houtgast and M. Steeneken’s publication “Predicting Speech Intelligibility in Rooms from the Modulation Transfer Function”, published in Acustica, Vol. 16, pp. 60-72, 1980. Modifications to the direct speech calculation scheme proposed in Chapter 4.1.1 are my original work. Speech vocal effort spectra in for the calculation of STI were obtained from ANSI S3.5-1997 “Methods for Calculation of the Speech Intelligibility Index”, published by the American National Standards Institute in New York. The data is presented in this thesis in Table 2.1. vi The Balanced Noise Criterion background noise spectra used in the calculation of STI were obtained from L. Beranek’s publication “Balanced noise-criterion (NCB) curves”, published in the Journal of the Acoustical Society of America, vol. 86, no. 2, in 1989. Human directivity factors used in the calculation of STI were obtained from R. Watson and O. Downey’s publication “The Little Red Book of Acoustics: A Practical Guide”, published by Blue Tree Acoustics in Sheffield, in 2008. The data is presented in this thesis in Table 2.3. The free-field distances shown in Table 2.5 were obtained from M. Hodgson’s and N. Heerema’s publication “Sound-Propagation Curves in Industrial Workrooms: Statistical Trends and Empirical Prediction Models”, published in Volume 3 of Building Acoustics in 1996. Modifications to the DL2 vs Distance model are my original work and are based on experimental data which was collected from a Healthcare Building Indoor Environment Quality (IEQ) study conducted by Dr. K. Bartlett, Dr. M. Hodgson, Dr. L. Scannell, Jinying Sun, Juliette Rauscher, and Denny Ng. Access to office buildings operated by Fraser Health (FH), Providence Health Care (PHC), Provincial Health Services Authority (PHSA) and Vancouver Coastal Health (VCH) was coordinated by Maureen Haddock and Rob Kolen. The data is presented in Chapter 3. I assisted in data collection and analysis as an intern student. vii Table of Contents Abstract ...............................................................................................................................................iii Lay Summary ....................................................................................................................................... iv Preface ................................................................................................................................................ v Table of Contents ............................................................................................................................... vii List of Tables .........................................................................................................................................x List of Figures ...................................................................................................................................... xi List of Supplementary Material ......................................................................................................... xiii Glossary ............................................................................................................................................. xiv Acknowledgements ......................................................................................................................... xviii 1 Introduction ................................................................................................................................ 1 1.1 Motivation ........................................................................................................................... 1 1.2 Acoustical Background Information .................................................................................... 2 1.2.1 Sources and Receivers ................................................................................................. 2 1.2.2 Sound Pressure Level (𝐿𝑝) ........................................................................................... 2 1.2.3 Addition and Subtraction of Sound Pressure Levels ................................................... 3 1.2.4 Frequency and Octave Bands ...................................................................................... 3 1.2.5 A-weighting ................................................................................................................. 4 1.2.6 Characterization of surfaces ........................................................................................ 4 1.2.7 Definition of a Room ................................................................................................... 5 1.2.8 Direct and Indirect Sound............................................................................................ 5 1.2.9 Reverberation Time (𝑅𝑇) ............................................................................................ 6 1.2.10 Decrease in Sound Pressure Level per Doubling of Distance (𝐷𝐿2) ........................... 7 1.2.11 Speech Transmission Index (𝑆𝑇𝐼) ................................................................................ 8 1.3 Literature Review ................................................................................................................ 8 1.3.1 𝐷𝐿2 for Predicting Noise Exposure ............................................................................. 8 viii 1.3.2 DL2 for Speech Applications ...................................................................................... 10 1.4 Scope ................................................................................................................................. 11 2 Theoretical 𝐷𝐿2 ........................................................................................................................ 13 2.1 Idealized 𝐷𝐿2 Model for STI .............................................................................................. 13 2.1.1 Fixed Model Components ......................................................................................... 13 2.1.2 Tentative Model Components .................................................................................. 14 2.1.3 Construction of DL2 Model ........................................................................................ 18 2.1.4 Sample Model Plots ................................................................................................... 20 2.2 𝐷𝐿2 Rating Scheme Alternatives ...................................................................................... 22 2.2.1 Room Purpose ........................................................................................................... 23 2.3 Conclusion ......................................................................................................................... 28 3 Experimental Verification .......................................................................................................... 30 3.1 𝐷𝐿2 in Real Rooms ............................................................................................................ 30 3.1.1 Motivation ................................................................................................................. 30 3.1.2 Methodology ............................................................................................................. 31 3.1.3 Uniform, Broadband Decay ....................................................................................... 34 3.1.4 Linear Decay .............................................................................................................. 38 3.1.5 𝐿𝑝, 1𝑚 ....................................................................................................................... 55 4 Complete 𝐷𝐿2 vs 𝑆𝑇𝐼 Model .................................................................................................... 63 4.1 Model Components ........................................................................................................... 63 4.1.1 Modulation Transfer Function (Direct Speech) ......................................................... 63 4.1.2 Experiment-Based Modifications to 𝐷𝐿2 Model ...................................................... 67 4.2 Model Construction........................................................................................................... 70 4.2.1 𝑆𝑇𝐼 vs Distance .......................................................................................................... 71 4.2.2 𝑆𝑇𝐼 vs 𝐷𝐿2 ................................................................................................................ 73 ix 4.3 Sample Applications .......................................................................................................... 75 4.3.1 Case 1 (Intelligibility) ................................................................................................. 75 4.3.2 Case 2 (Distraction) ................................................................................................... 78 4.3.3 Case 3 (Privacy) ......................................................................................................... 79 4.4 𝐷𝐿2 Observations ............................................................................................................. 81 4.4.1 Case 1 (Intelligibility) ................................................................................................. 81 4.4.2 Case 2 (Distraction) ................................................................................................... 82 4.4.3 Case 3 (Privacy) ......................................................................................................... 82 4.4.4 General Model Use Guideline ................................................................................... 83 4.5 Conclusions ....................................................................................................................... 83 5 Conclusion ................................................................................................................................. 85 6 Future Work .............................................................................................................................. 87 6.1 Speech Distraction ............................................................................................................ 87 6.2 Workplace Dividers ........................................................................................................... 87 Works Cited ....................................................................................................................................... 88 Appendix ........................................................................................................................................... 90 x List of Tables Table 1.1 - Full-octave octave band numbers and their associated frequencies in acoustics ............ 4 Table 1.2 - A-Weighting value for each Octave Band.......................................................................... 4 Table 1.3 - Reverberation Time Quantities and Calculation Thresholds ............................................. 7 Table 1.4 - Quality Ratings and STI Value Ranges for Speech Intelligibility (From IEC 60268-16) ...... 8 Table 2.1 - Speech Pressure Level (𝐿𝑝, 𝑠, 1𝑚, 0°) Spectrum for Male and Female Talkers at 1 m Directly in Front of a Human Talker's Mouth (From ANSI S3.5-1997 “Methods for Calculation of the Speech Intelligibilty Index” [12]) ....................................................................................................... 14 Table 2.2 - Octave Band 𝑆𝑇𝐼 Contributions [1] ................................................................................. 15 Table 2.3 - Octave Band Human Directivity Data (From R. Watson, O. Downey “The Little Red Book of Acoustics: A Practical Guide”, 2008 [13])...................................................................................... 16 Table 2.4 - Speech Sound Pressure Level (𝐿𝑝, 𝑠, 1𝑚, 𝑎𝑣𝑔) Spectrum for Male and Female Talkers at 1 m, Averaged over 360° ................................................................................................................... 16 Table 2.5 - Average and Standard Deviation (in Parentheses) for Free-Field Distances in Octave Bands for Empty, Fitted, and Fitted and Absorbent Industrial Rooms (From M. Hodgson, N. Heerema “Sound-Propagation Curves in Industrial Workrooms: Statistical Trends and Empirical Prediction Models” Building Acoustics, Vol. 3, 1996 [5]) .................................................................. 18 Table 2.6 - Sample 𝑆𝑇𝐼 Ranges and their Corresponding DL2 Values According to IEC 60268-16 .... 23 Table 2.7 - Quality Ratings for STI Based on Listening Effort [16] ..................................................... 25 Table 2.8 - Proposed Quality Ratings for Speech-Related Productivity Loss .................................... 27 Table 2.9 - Proposed Quality Ratings for Speech Privacy .................................................................. 28 Table 3.1 - Average 𝐷𝐿2, 𝑓 and 𝐷𝐿2, 𝑠, 𝐴 for (1) Open-plan Offices and (2) Standard Rooms in dB/DD. ............................................................................................................................................... 34 Table 3.2 - Average Difference between 𝐷𝐿2, 𝑓 and 𝐷𝐿2, 𝑠, 𝐴 for (1) Open-plan Offices and (2) Standard Rooms in dB/DD................................................................................................................. 35 Table 3.3 - Average Absolute Difference for 𝐷𝐿2, 𝑓 – 𝐷𝐿2, 𝑠, 𝐴for (1) Open-plan Offices and (2) Standard Rooms. ............................................................................................................................... 35 Table 3.4 - 𝐷𝐿2, 𝑠, 𝐴 Sensitivity to Deviations in Individual Octave Bands. ...................................... 37 Table 3.5 - Measured DL2 Grouped by Room Type, then by Divider Height for Open-plan Offices. 43 Table 3.6 - Average Absolute Regression Error Comparison Between Lp,S,A,1-16m and Lp,S,A,4m in dB. . 50 Table 3.7 - Maximum Regression Error Comparison Between Lp,S,A,1-16m and Lp,S,A,4m in dB. ............. 51 Table 4.1 - Assumptions Employed in the Idealized DL2 Model and their Conditions ...................... 67 Table 4.2 - Regression Equations Relating Sound Pressure Level at 1 m and Room Volume ........... 68 Table 4.3 - Average Difference for DL2,f - DL2,s,A for (1) Open-plan Offices and (2) Standard Rooms in dB/DD. ............................................................................................................................................... 69 xi List of Figures Figure 2.1 - Screenshot of Data Entry sheet of DL2 calculation tool ................................................. 19 Figure 2.2 - Screenshot of 𝑀𝑇𝐹 Calculation sheet of 𝐷𝐿2 calculation tool ..................................... 20 Figure 2.3 - Sample STI vs Distance Curve Evaluated at DL2 = 6 dB/DD ............................................ 21 Figure 2.4 - Sample STI vs DL2 Curve Evaluated at Distance = 4 m ................................................... 22 Figure 2.5 - Listening Effort vs. STI for 16 Normal-Hearing German Subjects for 120 German Sentences (Copied from J. Rennies and H. Schepker, "Listening Effort and Speech Intelligibility in Listening Situations Affected by Noise and Reverberation," Journal of the Acoustical Society of America, vol. 136, no. 5, pp. 2642-2653, 2014.) ............................................................................... 24 Figure 2.6 - Compiled Data and Prediction Model for Loss of Productivity (𝐷𝑃) vs 𝑆𝑇𝐼 (Copied from V. Hongisto, "A Model for Predicting the Effect of Speech of Varying Intelligibility on Work Performance," Indoor Air, vol. 15, pp. 458-468, 2005 [17]) .............................................................. 26 Figure 3.1 - Diagram showing signal chain for measuring reverberation time ................................. 32 Figure 3.2 - Diagram showing the typical measurement setup ........................................................ 33 Figure 3.3 - 𝐿𝑝, 𝑠, 𝐴, 𝑒𝑥𝑝 vs Distance for Open-plan Offices (1.2 m < 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 < 1.3 m). ............... 40 Figure 3.4 - 𝐿𝑝, 𝑠, 𝐴, 𝑒𝑥𝑝 vs Distance for Open-plan Offices (𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 = 1.4 m). ............................ 40 Figure 3.5 - 𝐿𝑝, 𝑠, 𝐴, 𝑒𝑥𝑝 vs Distance for Open-plan Offices (𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 = 1.5 m). ............................ 41 Figure 3.6 - 𝐿𝑝, 𝑠, 𝐴, 𝑒𝑥𝑝 vs Distance for Open-plan Offices (1.6 m < 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 < 1.8 m). ............... 41 Figure 3.7 - 𝐿𝑝, 𝑠, 𝐴, 𝑒𝑥𝑝 vs Distance for Open-plan Offices (𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 > 2 m). ............................... 42 Figure 3.8 - 𝐿𝑝, 𝑠, 𝐴, 𝑒𝑥𝑝 vs Distance for Standard Rooms. ............................................................... 42 Figure 3.9 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑆, 𝐴, 1 − 16𝑚 (Open-plan Offices, 1.2 m < 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 < 1.3 m). ............................................................................................................................................... 44 Figure 3.10 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑆, 𝐴, 1 − 16𝑚 (Open-plan Offices, 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 = 1.4 m). ........................................................................................................................................................... 44 Figure 3.11 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑆, 𝐴, 1 − 16𝑚 (Open-plan Offices, 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 = 1.5 m). ........................................................................................................................................................... 45 Figure 3.12 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑆, 𝐴, 1 − 16𝑚 (Open-plan Offices, 1.6 m < 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 < 1.8 m). ............................................................................................................................................... 45 Figure 3.13 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑆, 𝐴, 1 − 16𝑚 (Open-plan Offices, 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 > 2 m). 46 Figure 3.14 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑆, 𝐴, 1 − 16𝑚 (Standard Rooms). ............................... 46 Figure 3.15 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑠, 4𝑚 (Open-plan Offices, 1.2 m < 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 < 1.3 m). ........................................................................................................................................................... 47 Figure 3.16 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑠, 4𝑚 (Open-plan Offices, 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 = 1.4 m). .......... 47 Figure 3.17 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑠, 4𝑚 (Open-plan Offices, 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 = 1.5 m). .......... 48 Figure 3.18 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑠, 4𝑚 (Open-plan Offices, 1.6 m < 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 < 1.8 m). ........................................................................................................................................................... 48 Figure 3.19 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑠, 4𝑚 (Open-plan Offices, 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 > 2 m). ............. 49 Figure 3.20 - 𝐷𝐿2 Regression Error for 𝐷𝐿2, 𝑠, 4𝑚 (Standard Rooms). ............................................ 49 xii Figure 3.21 - 𝐿𝑝, 1𝑚 - 𝐿𝑝, 1𝑚, 𝐹𝐹 for 125 Hz Band. ......................................................................... 57 Figure 3.22 - 𝐿𝑝, 1𝑚 - 𝐿𝑝, 1𝑚, 𝐹𝐹 for 250 Hz Band. ......................................................................... 57 Figure 3.23 - 𝐿𝑝, 1𝑚 - 𝐿𝑝, 1𝑚, 𝐹𝐹 for 500 Hz Band. ......................................................................... 58 Figure 3.24 - 𝐿𝑝, 1𝑚 - 𝐿𝑝, 1𝑚, 𝐹𝐹 for 1,000 Hz Band. ...................................................................... 58 Figure 3.25 - 𝐿𝑝, 1𝑚 - 𝐿𝑝, 1𝑚, 𝐹𝐹 for 2,000 Hz Band. ...................................................................... 59 Figure 3.26 - 𝐿𝑝, 1𝑚 - 𝐿𝑝, 1𝑚, 𝐹𝐹 for 4,000 Hz Band. ...................................................................... 59 Figure 3.27 - 𝐿𝑝, 1𝑚 - 𝐿𝑝, 1𝑚, 𝐹𝐹 for 8,000 Hz Band. ...................................................................... 60 Figure 4.1 - Screenshot of Data Entry sheet of finalized DL2 calculation tool ................................... 70 Figure 4.2 - Sample STI vs Distance plot for an Open Plan Office ..................................................... 72 Figure 4.3 - Sample STI vs Distance plot for a Standard Room ......................................................... 73 Figure 4.4 - Sample STI vs DL2 plot showing Artefact of Decibel Subtraction around 6 dB/DD Range ........................................................................................................................................................... 74 Figure 4.5 - Sample 𝑆𝑇𝐼 vs 𝐷𝐿2 plot with E336-15 Adjustment for Decibel Subtraction Approximation for Low 𝑆/𝑁 ............................................................................................................. 75 Figure 4.6 - 𝑆𝑇𝐼 vs 𝐷𝐿2 at 10 m from a talker for a compliant classroom (𝐿𝑛 = 35 dBA, 𝑇 = 0.8 s) 76 Figure 4.7 - 𝑆𝑇𝐼 vs 𝐷𝐿2 at 10 m from a talker for a non-compliant classroom (𝐿𝑛 = 40 dBA, 𝑇 = 1.0 s) ........................................................................................................................................................ 77 Figure 4.8 - 𝑆𝑇𝐼 vs Distance for hypothetical non-compliant classroom in Figure 4.7 (𝐿𝑛 = 35 dBA, 𝑇 = 0.8 s) ............................................................................................................................................ 78 Figure 4.9 - 𝑆𝑇𝐼 vs 𝐷𝐿2 at distances of 4, 6, 8 and 10 m for a hypothetical study room (𝐿𝑛 = 30 dBA, 𝑇 = 0.8 s) ................................................................................................................................... 79 Figure 4.10 - 𝑆𝑇𝐼 vs 𝐷𝐿2 at 4 m for a hypothetical eating establishment without booths (𝐿𝑛 = 40 dBA, 𝑇 = 1 s) ...................................................................................................................................... 80 Figure 4.11 - 𝑆𝑇𝐼 vs 𝐷𝐿2 at 4 m for eating establishment with booths at varying noise levels (𝐿𝑛 = 40 dBA, 𝑇 = 1 s) ................................................................................................................................. 81 xiii List of Supplementary Material Microsoft Excel spreadsheet for Speech Transmission Index (STI) vs. Distance calculation tool Microsoft Excel spreadsheet for Speech Transmission Index (STI) vs. DL2 calculation tool xiv Glossary 𝛼 – Absorption coefficient of a surface, defined from 0 – 1 𝛼𝑆𝑇 – Average surface absorption of a room 𝛼𝑐 – Ceiling absorption, defined from 0 – 1 𝛼𝑓 – Apparent furnishing absorption, defined from 0 – 1 𝐶𝐼𝑆 – Common Intelligibility Scale dBA – A-weighted sound pressure level 𝛿(𝑡) – The dirac-pulse function 𝐷𝐿2 – Decrement of sound pressure level per doubling of distance, in dB/DD 𝐷𝐿2,𝑓 - 𝐷𝐿2 of frequency band 𝑓, in dB/DD 𝐷𝐿2,𝑠,𝐴 – 𝐷𝐿2 of A-weighted speech pressure level, in dB/DD 𝐷𝐿2,𝑠,4𝑚 – 𝐷𝐿2 of speech pressure level starting at a distance of 4 m, in dB/DD 𝐷𝐿2,𝑠,𝐴,1−16𝑚 – 𝐷𝐿2 of speech pressure levels between distances of 1 – 16 m, in dB/DD 𝐷𝑃 – Loss in productivity, in % 𝐸𝐷𝑇 – Early decay time, in seconds 𝑓 – Frequency, in Hertz 𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟 – Height of office divider, in metres Hz – Frequency, in Hertz 𝐿 – Sound pressure or power level, in dB 𝐿𝐴,𝑠,1𝑚 – A-weighted speech pressure level evaluated at a distance of 1 m, in dB 𝐿𝑛 – background noise level, in dB 𝐿𝑝 – Sound pressure level, in dB – relative to 2x10-5 pascals 𝐿𝑝,1𝑚 – The sound pressure level at a distance of 1 m from a source, in dB 𝐿𝑝,1𝑚,𝐹𝐹 – The sound pressure level at a distance of 1 m from a source in a free field, in dB xv 𝐿𝑝,𝑑𝑖𝑟𝑒𝑐𝑡 – Direct sound pressure level of a sound source 𝐿𝑝,𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡 – Indirect sound pressure level in a room resulting from a sound source 𝐿𝑝,𝑡𝑜𝑡𝑎𝑙 – Total sound, comprising both direct and indirect sound 𝐿𝑝,𝑠,4𝑚 – A-weighted speech pressure level evaluated at a distance of 4 m, in dB 𝐿𝑝,𝑠,1𝑚,0° – Speech pressure level measured at a distance of 1 m, and at direct incidence, in dB 𝐿𝑝,𝑠,1𝑚,𝑎𝑣𝑔 – Average speech pressure level at a distance of 1 m, in dB 𝐿𝑝,𝑎𝑣𝑔 – Sound pressure level averaged over 360° around a source, in dB 𝐿𝑝,0° - Sound pressure level at direct incidence (0°) from a source, in dB 𝐿𝑝,𝑆,𝐴,𝑒𝑥𝑝 – Measured speech pressure level along a 𝐷𝐿2 curve 𝐿𝑝,𝑆,𝐴,𝑟𝑒𝑔 – Predicted speech pressure level according to a 𝐷𝐿2curve 𝐿𝑤 – Sound power level, in dB – relative to 10-12 watts 𝑚(𝑓) – The modulation transfer function evaluated at frequency 𝑓 𝑁 – Total number of measurements in a series of measurements for calculating 𝐷𝐿2 NCB – Balanced Noise Criterion contours, spectra for describing HVAC noise in occupied rooms NC – Noise Criterion contours, spectra for describing HVAC noise in unoccupied rooms 𝜌 – Reflection coefficient of a surface, defined from 0 – 1 𝑃𝑟𝑒𝑓 – Reference sound pressure level – 2x10-5 pascals 𝑃𝑟𝑚𝑠 – Room mean squared pressure, used in calculation of sound pressure level 𝑄𝛳 – Source directivity factor 𝑄𝑡 – Directivity index of a talker 𝑄𝑙 – Directivity index of a listener 𝑟 – Distance, in metres 𝑟(𝑡) – The total squared impulse response for a room xvi 𝑟0 – Distance of first 𝐿𝑝 measurement in a series of 𝐿𝑝 measurements for calculating 𝐷𝐿2 𝑟𝑐 – Critical radius, defined as the distance where indirect direct sound are equal, in metres 𝑟𝑑(𝑡) – The direct sound contribution to the room impulse response 𝑟𝑑 – Distraction distance, in metres 𝑟𝑖(𝑡) – The indirect sound contribution to the room impulse response 𝑟𝑛 – Distance of 𝐿𝑝 measurement in a series of 𝐿𝑝 measurements for calculating 𝐷𝐿2 𝑟𝑝 – Privacy distance, in metres 𝑟𝑡𝑟 – The transition distance, where the intelligibility rating classification changes, in metres 𝑅𝐼𝑅 – Room impulse response 𝑅𝐼𝑅𝑟𝑒𝑎𝑙 – Real room impulse response 𝑅𝐼𝑅𝑠𝑖𝑚 – Simulated room impulse response 𝑅𝐼𝑅𝑤𝑛 – Room impulse response generated using white noise 𝑅𝑇, 𝑇 – Reverberation time, typically refers to 𝑇20 𝑠 – Seconds 𝑠 – Scattering coefficient 𝑆 – Surface area of a room 𝑆𝐼𝐼 – Speech Intelligibility Index 𝑆𝐿𝐴 – A-weighted speech pressure level, in dB 𝑆/𝑁 – The signal to noise ratio 𝑆/𝑁𝑎𝑝𝑝 – The apparent signal to noise ratio, truncated at -15 dB, and 15 dB 𝑆𝑃 – Sound propagation, in dB/DD, see also: 𝐷𝐿2 𝑆𝑇𝐼 – Speech Transmission Index, defined from 0 – 1 𝑆𝑇𝐼𝑓 – The speech transmission index at frequency 𝑓 𝑡 – Time, in seconds xvii 𝜏 – Transmission coefficient of a wall or divider, defined from 0 – 1 𝑇20 – Reverberation time calculated from first 20 dB of sound decay starting at -5 dB 𝑇30 – Reverberation time calculated from first 30 dB of sound decay starting at -5 dB 𝑇60 – Reverberation time calculated from 60 dB of sound decay starting at -5 dB xviii Acknowledgements I would like to express my sincerest gratitude to the late Dr. Murray Hodgson for inviting me to study as a graduate student and providing me with his unconditional support and guidance throughout my studies. I would also like to thank Shira Daltrop for agreeing to be the technical expert on my defense committee and taking time out of her personal life to help review this thesis. I would not have been able to finish my degree if it weren’t for her support during the final phases of my studies. Finally, I would like to thank Dr. Steven Rogak for acting as my supervisor. In the absence of an entity overseeing the progress of my thesis, I had halted all work. It is thanks to his support that I was able to figure out the logistics of finishing my degree. 1 1 Introduction 1.1 Motivation Current methods for acoustical characterization of rooms are based on the following set of parameters: background noise level, signal level, and reverberation time. These parameters make up the temporal and steady-state characterization at specific locations in a room. However, the spatial characteristics of the sound field are unaddressed without the use of numerical modeling. In the case of listening situations such as classrooms, a minimalist assessment will focus only on a limited number of talker-listener position pairs such as a talker at the front of the classroom and the closest seat, then the farthest seat. The assessment may find that the front row has excellent speech intelligibility and that the back row has poor speech intelligibility – the speech intelligibility at intermediate positions remains unaccounted for. In cases where funds for remedial work is limited, knowing the spatial characteristics of sound in a room could facilitate better use without the need for extraneous expenditures. The decay of sound pressure per doubling of distance (𝐷𝐿2, in dB/DD) characterizes the behaviour of sound as a function of distance. Since 𝐷𝐿2 is a property of the room (resulting from room geometry, sound absorption characteristics, and surface sound scattering characteristics) it can be assumed that the rate of sound decrement from any source is identical regardless of where it is located or the direction of propagation. The sound pressure level (𝐿𝑝) at any location can be predicted if the number of sound sources, their sound power levels (𝐿𝑤), and distances (𝑟) from a receiver are known. In cases with normal human talkers, an average human talker sound power spectrum may be assumed. 𝐷𝐿2 can be thought of as how sources and receivers are connected or disconnected, regardless of whether the sound is useful or detrimental. For a given speaker-listener distance, 𝐷𝐿2 will indicate whether the speaker will be connected (intelligible, audible) or disconnected (unintelligible, inaudible). Understanding the factors which affect 𝐷𝐿2 will facilitate better acoustical design in rooms. 2 Therefore, adoption of 𝐷𝐿2 is proposed as a universal room acoustics parameter. As opposed to spot measurements, where intuition is required to select suitable measurement locations, 𝐷𝐿2 is a spatial property by definition and a single series of measurements spanning the length of a room is expect to suffice in approximating a room’s acoustical environment. It is therefore of interest to investigate a method for applying 𝐷𝐿2 to rooms. In addition, developing rating schemes based on 𝐷𝐿2 will provide users with an intuitive evaluation method. 1.2 Acoustical Background Information The following subsections will explain the basic quantities and principles used in acoustics. Advanced quantities and principles specific to this thesis will be explained as they are introduced. 1.2.1 Sources and Receivers Fluctuations in pressure in fluids are perceived as sound. In acoustics, sources of pressure fluctuations (such as loudspeakers, human talkers, etc.) are referred to as sources and receptors of sound (human listeners, microphones, etc.) are referred to as receivers. 1.2.2 Sound Pressure Level (𝐿𝑝) Sound pressure level (𝐿𝑝) is the main quantity of interest in acoustics. It is related to the physical amplitude of sound waves and the loudness of sound. The amplitude refers to the absolute maximum pressure and is therefore quantified in Pascals (Pa). Since the range of pressure fluctuations detectable by the human ear spans several orders of magnitude, 𝐿𝑝 is quantified in a logarithmic term referred to as decibels (dB). As all logarithmic terms are relative, 𝐿𝑝 is calculated from the root mean square of a pressure fluctuation (𝑃𝑟𝑚𝑠2 ) in relation to the 𝑃𝑟𝑚𝑠2 of the lowest sound pressure audible to human beings (𝑃𝑟𝑒𝑓2 ) using Eq. (1.1). 𝐿𝑝 is a term used to quantify all sounds whether beneficial (e.g. speech) or harmful (e.g. noise). 𝐿𝑝 = 10 𝑙𝑜𝑔 (𝑃𝑟𝑚𝑠2𝑃𝑟𝑒𝑓2 ) (1.1) Where: 𝑃𝑟𝑚𝑠 is the room mean square pressure 3 𝑃𝑟𝑒𝑓 is the reference pressure, which is equal to 2x10-5 Pa. This is cited to be the lowest audible level for a human of normal hearing at 1,000 Hz. 1.2.3 Addition and Subtraction of Sound Pressure Levels As sound pressure levels are logarithmic terms, they cannot be added or subtracted arithmetically. Addition and subtraction operations are done logarithmically as shown in Eq. (1.2) and Eq. (1.3). 𝐿1+2 = 10 𝑙𝑜𝑔 (10(𝐿110) + 10(𝐿210)) (1.2) 𝐿1−2 = 10 𝑙𝑜𝑔 (10(𝐿110) − 10(𝐿210)) (1.3) Where: 𝐿1 and 𝐿2 are sound pressure levels in decibels. Note that the summation of two sound pressure levels which differ by 10 dB results in a value that is 0.5 dB greater than the higher sound pressure level. For example, the logarithmic sum of 50 dB and 60 dB is 60.5 dB. In acoustics, a signal can be considered negligible if it is 10 dB lower than another. 1.2.4 Frequency and Octave Bands Frequency, in Hertz (Hz), is related to the human perception of pitch. The audible frequency range in humans is 20 to 20,000 Hz. Predetermined ranges of frequencies are combined into bins called bands. In acoustics, the bands are referred to as octave bands and third octave bands. The term octave is derived from the Latin term octavus, or eighth, and is defined as the interval between two pitches where the second pitch is double that of the first. In acoustics, each band’s centre frequency is double that of the previous band, and the bandwidth increases with increasing frequency. Acoustics also makes use of third-octave bands, where the bins are reduced in size. The sound pressure level of an octave band is the sum all the pressure levels of its constituent frequencies. Table 1.1 shows the standard octave band numbers and centre-frequency of full octave bands used in acoustics. 4 Table 1.1 - Full-octave octave band numbers and their associated frequencies in acoustics Band number 1 2 3 4 5 6 7 8 Frequency [HZ] 63 125 250 500 1,000 2,000 4,000 8,000 1.2.5 A-weighting Despite being of the same sound pressure level, sounds of different frequencies are perceived as being different in loudness. The perceived loudness as a function of frequency is due to the physical makeup of the human auditory system. The A-weighting network is a series of frequency-dependent correction factors that are used to adjust measured sound pressure levels to represent what humans will perceive. The A-weighting network correction factors and their corresponding centre frequencies and are shown in Table 1.2. The adjustments are simply added or subtracted to the octave-band sound pressure level. The resulting values are referred to as the A-weighted sound pressure level, notated as dBA. Table 1.2 - A-Weighting value for each Octave Band Octave band 125 250 500 1,000 2,000 4,000 8,000 16,000 WEIGHTING [DB] -16.1 -8.6 -3.2 0 1.2 1.0 -1.1 -6.6 The A-weighted sound pressure level (dBA) of a signal is then the A-weighted octave-band sound pressure levels summed in accordance to Eq. (1.2). 1.2.6 Characterization of surfaces All surfaces can be defined acoustically using the following quantities: absorptivity (𝛼) the percentage of incident sound on a surface that is absorbed and then converted either to heat or vibration; transmissivity (𝜏) the percentage of incident sound on a surface that is transmitted to the other side as sound; reflectivity (𝜌) the percentage of incident sound that is reflected. Each of these quantities range from 0 to 1, and their sum is 1. Reflectivity is then further defined by its scattering coefficient (𝑠). The scattering coefficient ranges from 0 to 1. With a scattering coefficient of 0, the incident sound is reflected specularly and is 5 likened to light reflected by a mirror. With a scattering coefficient of 1, the incident sound is scattered randomly, and the amount of sound being reflected is equal in all directions. 1.2.7 Definition of a Room A room is defined as a space enclosed by a floor, walls and a ceiling, typically for human occupation. For the acoustics inside an individual room, the relevant parameters are the absorptivity and scattering coefficients. 1.2.8 Direct and Indirect Sound Sound is typically categorized as being direct or indirect. In rooms, sound that is reflected off of a surface is considered to be indirect sound (𝐿𝑝,𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡). Conversely, sound that reaches a receiver without being reflected is called direct sound (𝐿𝑝,𝑑𝑖𝑟𝑒𝑐𝑡). Except for engineered environments such as anechoic chambers, or at a large distance from any surface, direct sound is rarely found isolated from indirect sound. The combination of direct and indirect sound is referred to as the total sound (𝐿𝑝,𝑡𝑜𝑡𝑎𝑙). According to diffuse field theory, the total sound pressure level due to a point source in a room can be predicted using Eq. (1.4): 𝐿𝑝,𝑡𝑜𝑡𝑎𝑙 = 𝐿𝑤 + 10𝑙𝑜𝑔 [𝑄𝛳4𝜋𝑟2+4(1 − 𝛼𝑆𝑇)𝑆𝛼𝑆𝑇] (1.4) Where: 𝐿𝑤 is the source power level in decibels relative to the reference sound power level of 10-12 watts 𝑄𝜃 is the source directivity factor, which equals 1 for omnidirectional point sources 𝑟 is the source-receiver distance in m 𝑆 is the total surface area of the room 𝛼𝑆𝑇 is the room averaged absorption coefficient Within the logarithmic argument are the direct-field and reverberant (indirect) field contributions, respectively. 6 When considering only direct sound (i.e. in a free-field), only the first term of the logarithmic argument remains. Then for omnidirectional point sources, 𝑄𝜃 is 1, resulting in Eq. (1.5).This form is also useful for sound source calibrations, which are undertaken in approximated free-field environments known as Anechoic chambers. For calibration measurements at 1 m, the logarithmic term becomes zero, and the sound power level is simply the average sound pressure level plus 11 dB. For every doubling of distance, 𝐿𝑝,𝑑𝑖𝑟𝑒𝑐𝑡 decreases by 6 dB. This behavior is also known as the inverse square law. The 6 dB decay per doubling of distance is constant regardless of environment for the direct sound component of an omnidirectional point source in three dimensional space. 𝐿𝑝,𝑑𝑖𝑟𝑒𝑐𝑡 = 𝐿𝑤 − 11 − 10𝑙𝑜𝑔(𝑟2) (1.5) Conversely, the reverberant field contribution does not include any distance terms, suggesting that the reverberant sound pressure level is constant at all distances from a source. However, this generally only occurs in an engineered environment known as a reverberation chamber. Reverberation chambers are designed such that the room is nearly cubic in geometry, is large in volume, has hard reflective surfaces only, and have sound scattering surfaces distributed throughout the volume of the chamber. The conditions required to achieve a uniform reverberant field are rarely satisfied by real rooms. Real rooms are rarely cubic in geometry and acoustically absorptive surfaces are typically unevenly distributed. As such, the indirect sound is typically calculated by logarithmic subtraction of the calculated direct sound (using 𝐿𝑤) from the measured total sound in accordance with Eq. (1.3), resulting in Eq. (1.6). 𝐿𝑝,𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡 = 10𝑙𝑜𝑔(10(𝐿𝑝,𝑡𝑜𝑡𝑎𝑙/10) − 10(𝐿𝑝,𝑑𝑖𝑟𝑒𝑐𝑡/10)) (1.6) 1.2.9 Reverberation Time (𝑅𝑇) Reverberation time (𝑅𝑇) quantifies the temporal decay of sound. It is defined as the time required for sound pressure level to decrease by 60 dB. Measuring 60 dB of decay requires that the signal exceed the background noise level by 60 dB in every band, which is difficult to achieve in practice. Instead, the reverberation time is approximated by measuring the decay time between two 7 thresholds and extrapolating to 60 dB. Common reverberation time calculation schemes are shown in Table 1.3. Table 1.3 - Reverberation Time Quantities and Calculation Thresholds 𝐑𝐓 Scheme Start Threshold [dB] End Threshold [dB] Early Decay Time (𝐄𝐃𝐓) 0 -10 𝐓𝟐𝟎 -5 -25 𝐓𝟑𝟎 -5 - 35 As Early Decay Time (𝐸𝐷𝑇) is based on the first 10 dB of decay, it is highly affected by local surfaces. 𝐸𝐷𝑇 is expected to vary immensely with location in a room. 𝑇20 and 𝑇30 exclude the first 5 dB, and extrapolate over a larger range, making them more representative of the average reverberation time. 𝑇20 is widely used in acoustical engineering. 1.2.10 Decrease in Sound Pressure Level per Doubling of Distance (𝐷𝐿2) 𝐷𝐿2 is the rate of spatial decay of sound and is defined as the decrease in sound pressure level per doubling of distance (dB/DD) from a source. 𝐷𝐿2 is calculated using Eq. (1.7). For reference, free-field decay for an omnidirectional point source in 3-dimensional space (as introduced in Section 1.2.8) has a 𝐷𝐿2 value of 6 dB/DD. Typical presentation of data for 𝐷𝐿2 involves plotting sound pressure level on a base-2 logarithmic scale for easy comparison to the free-field case. Moreover, logarithmic regressions are favorable over linear regressions as experimental data suggests that sound typically decays exponentially with distance. 𝐷𝐿2 = − 𝑙𝑜𝑔10(2)𝑁 ∑ [𝐿𝑝,𝑛 𝑙𝑜𝑔10 (𝑟𝑛𝑟0)] − ∑ 𝐿𝑝,𝑛 ∑ 𝑙𝑜𝑔10 (𝑟𝑛𝑟0)𝑁𝑛=1𝑁𝑛=1𝑁𝑛=1𝑁 ∑ [𝑙𝑜𝑔10 (𝑟𝑛𝑟0)]2− [∑ 𝑙𝑜𝑔10 (𝑟𝑛𝑟0)𝑁𝑛=1 ]2𝑁𝑛=1 (1.7) Where: 𝑁 is the total number of sound pressure level data points 𝐿𝑝,𝑛 is the sound pressure level at data point 𝑛 8 𝑟𝑛 is the distance at which 𝐿𝑝,𝑛 was measured 𝑟0 is the initial (or smallest) measurement distance 1.2.11 Speech Transmission Index (𝑆𝑇𝐼) Speech Transmission Index (𝑆𝑇𝐼) is a measure developed by Houtgast and Steeneken to quantify the quality of speech at a listener position [1]. It is based on a technique used in optics called the Modulation Transfer Function (𝑀𝑇𝐹) and assesses the degradation of speech signal integrity due to noise and reverberation time. Increasing noise and reverberation time reduces intelligibility. 𝑆𝑇𝐼 is rated on a scale of 0 to 1, with 0 being totally unintelligible, and 1 being perfectly intelligible with no signal degradation. Table 1.4 - Quality Ratings and STI Value Ranges for Speech Intelligibility (From IEC 60268-16) STI Rating Bad Poor Fair Good Excellent 𝑺𝑻𝑰 Range 0.00 – 0.30 0.30 – 0.45 0.45 – 0.60 0.60 – 0.75 0.75 – 1.00 1.3 Literature Review Prior to its current name of 𝐷𝐿2, sound decrement per doubling of distance was introduced by Sharland as an estimate for sound propagation in open-plan offices [2]. Free-field decrement of 6 dB per doubling of distance was used as a comparison for the sound decrement in open-plan offices. Sharland’s theoretical analysis of a sound source in an open-plan office resulted in an expected decrement of 3 dB per doubling of distance. In addition to its application in open-plan offices, 𝐷𝐿2 was used to predict noise exposure due to equipment in industrial rooms. 𝐷𝐿2 has been described using different terms throughout its use, and all descriptions of existing work will use the original terminology and conventions. When referring to 𝐷𝐿2, increasing 𝐷𝐿2 magnitude means an increasing rate of decrease in sound pressure level. Sound propagation is the converse of 𝐷𝐿2: when 𝐷𝐿2 is high, sound propagation is low, and vice versa. 1.3.1 𝐷𝐿2 for Predicting Noise Exposure In 1981, Lindqvist presented experimental sound pressure level data versus distance on a logarithmic scale [3]. A logarithmic distance scale was used for direct comparison to point-source 9 free-field decay of 6 dB per doubling of distance. While logarithmic regressions were not applied to the data, Lindqvist made extensive reference to the rate of spatial sound decay, and factors that influenced it. Lindqvist observed that values of sound decay approached 6 dB/DD as absorption increased, but never exceeded it. Hodgson used the term sound propagation (𝑆𝑃) to describe the decay of sound pressure level per doubling of distance in four industrial rooms under unfitted, partially fitted, and fully fitted conditions in 1983 [4]. Sound propagation was found to be insensitive to direction of propagation when the roof is not pitched. When the roof is pitched, sound propagation varied with direction in the room. This was theorized to be caused by either the pitched roof reflecting sound back towards the source, or away from it depending on the pitch direction. In the smallest factory, sound propagation decreased with increasing fitting density. At maximum fitting density, a secondary slope appeared in the sound propagation – that is, the value of sound propagation changed a some distance from the source. In other cases, the sound propagation was single-sloped and decreased when fittings were introduced. However, the sound propagation for partial and fully fitted rooms was similar. Hodgson et. al. then created an empirical model for predicting sound propagation curves in industrial rooms using experimental data in 1996 [5]. The model accounted for a change in slope in sound propagation by dividing the total sound propagation curve into an initial and final slope. Experimental data showed that the initial slope had values ranging from 2-5 dB/DD, and the final slope had values ranging from 4-9 dB/DD. Ondet et. al. modeled sound propagation in industrial rooms using RAYSCAT, a ray tracing model in 1989 [6]. RAYSCAT was used to study the effect of fitting distribution and absorption. As expected, 𝑃𝑑𝑑 (equivalent to 𝑆𝑃 and the inverse of 𝐷𝐿2) decreased when fittings were introduced, and sound propagation was lowest in rooms of high fitting density. Ondet et. al. then developed assessment criterion by parametric analysis of industrial rooms using RAYSCAT in 1995 [7]. The results were verified using experimental data from 200 rooms, whose 𝑃𝑑𝑑 values ranged from 1.5-4.5 dB/DD for both treated and untreated rooms. 10 1.3.2 DL2 for Speech Applications In 1999, Hodgson measured propagation of speech using sound propagation in university classrooms as part of a speech quality assessment using speech intelligibility index, signal to noise ratio, and reverberation time [8]. Octave-band sound pressure levels were measured, A-weighted, and summed to yield the A-weighted Speech pressure level (𝑆𝐿𝐴). Sound propagation was then calculated, yielding values of 1.1 dB/DD, 1.0 dB/DD, 1.6 dB/DD, and 2.4 dB/DD in four classrooms. Hodgson also produced an empirical model for predicting sound propagation for A-weighted speech levels in classrooms [9]. The model used the length, height, and presence of basic acoustical treatment to predict sound propagation. The prediction was applied to small and large classrooms of low and high absorption, resulting in measured/predicted sound propagation values of -0.6/-0.6 dB/DD for small rooms of low absorption, -1.4/-1.8 dB/DD large rooms of low absorption, -1.8/-1.7 dB/DD small rooms of high absorption, and -2.6/-3.0 dB/DD for large rooms of high absorption. Current applications of 𝐷𝐿2 focus on speech distraction in open-plan offices. Keranen measured 𝐷𝐿2 in 16 open-plan offices to propose a standardized measurement method and quality metrics [10]. Like Hodgson’s work in classrooms, Keranen calculated 𝐷𝐿2 for the A-weighted speech pressure level (𝐷𝐿2,𝑠,𝐴). It was observed that 𝐷𝐿2 in open-plan offices is like 𝐷𝐿2 in furnished industrial rooms as both feature a change in 𝐷𝐿2 at some distance from a source. To avoid the change in 𝐷𝐿2, Keranen proposed that 𝐷𝐿2 be measured from 4 m and beyond (𝐷𝐿2,𝑠,4𝑚), and to measure the speech pressure levels at 4 m (𝐿𝑝,𝑠,4𝑚). Using these two values, Keranen used 𝑆𝑇𝐼 to introduce two new quantities called the distraction distance (𝑟𝑑) and the privacy distance (𝑟𝑝). 𝑟𝑑 and 𝑟𝑝 are the distances from a talker until which speech is distracting (𝑆𝑇𝐼 > 0.50), and until which speech is confidential (𝑆𝑇𝐼 < 0.20). 𝐷𝐿2,𝑠,4𝑚 values ranged from 4 dB/DD to 12.4 dB/DD, 𝑟𝑑 ranged from 5.4 m to 18.5m, and 𝑟𝑝 ranged from 11.9 m to 32.6 m. It should be noted that 𝑟𝑝 exceeded the maximum room length in 6 cases. This work is the foundation for ISO 3382-3. Using the same set of experimental data, Keranen produced an empirical model for predicting 𝐿𝑝,𝑠,4𝑚, 𝐷𝐿2,𝑠,4𝑚, and 𝑟𝑑 [11]. The model uses the room length (𝐿), room width (𝑊), room height (𝐻), average screen height (ℎ), ceiling absorption (𝛼𝑐), apparent furnishing absorption (𝛼𝑓) and 11 speech effort (𝐿𝐴,𝑆,1𝑚). Prediction accuracy was cited to be 3.0 dB, 1.5 dB/DD and 2.5 m for 𝐿𝑝,𝑠,4𝑚, 𝐷𝐿2,𝑠,4𝑚, and 𝑟𝑑 respectively. 1.4 Scope Much work has been done on 𝐷𝐿2 in specific areas such as noise prediction in industrial rooms, or speech distraction in open-plan offices. 𝐷𝐿2 has also been measured in very short distances in classrooms, suggesting that it may also be useful in quantifying listening quality of rooms in the same way it can quantify speech privacy. This thesis aims to generalize the use of 𝐷𝐿2 as a quality metric for unamplified speech in all rooms. The proposed work was separated into three components: a theoretical section, an experimental section, and an applications section. The theoretical section aimed to develop a base model for 𝐷𝐿2 and develop a set of rating criteria, the second component aimed to validate the 𝐷𝐿2 model, and the third component refined the model and applied it to sample rooms. An idealized model for 𝐷𝐿2 was implemented as a tool in Microsoft Excel. The model calculates 𝑆𝑇𝐼 at all points along the sound propagation curve in a room. The model was based on an intial set of assumptions and idealizations. The intent was to use experimental data to either correct the model or better understand its limitations. The initial model was then used to test initial quality rating schemes. Like the work conducted by Virjonen and Hongisto, the rating schemes aimed to use speech-related metrics such as 𝑆𝑇𝐼. However, as 𝑆𝑇𝐼 quality ratings span large ranges of values, metrics that are intuitive to lay readers were also investigated. This was intended to give commissioners more insight into how their spaces perform acoustically. 𝐷𝐿2 data collected in real rooms was then used to examine the behavior of sound in a wide variety of acoustical environments and furnishing arrangements. Observed trends in the data were used to improve the idealized 𝐷𝐿2 model to better reflect conditions found in real rooms. The data was also used to propose a suitable 𝐷𝐿2 measurement range in rooms. 12 Finally, as a proof of concept, the refined 𝐷𝐿2 model was used to evaluate a sample of hypothetical rooms. The recommendations were compared with observed 𝐷𝐿2 values to assess the reasonability of the recommendations. 13 2 Theoretical 𝐷𝐿2 2.1 Idealized 𝐷𝐿2 Model for STI An initial, idealized model was developed and implemented in Microsoft Excel to assess how 𝐷𝐿2 affects 𝑆𝑇𝐼 as a function of distance from a speech source. In this iteration, 𝑆𝑇𝐼 is calculated using only the reverberant speech at various distances from a source and was therefore only applicable to large source-receiver distances or in rooms where the source is physically obstructed. The speech sound pressure levels used to calculate 𝑆𝑇𝐼 at each distance increment were calculated assuming a standard human talker power spectrum decaying at a constant 𝐷𝐿2. The main objective of this model was to examine how 𝐷𝐿2 and 𝑆𝑇𝐼 are related – that is: (1) how 𝑆𝑇𝐼 varies with distance for a given value of 𝐷𝐿2, and (2) how 𝑆𝑇𝐼 varies at a single position for different values of 𝐷𝐿2. The model was based on assumptions and idealizations, and was used to explore possible applications of 𝐷𝐿2 as a parameter. These idealizations were assessed and refined in later chapters using experimental data. 2.1.1 Fixed Model Components The components of the model listed in this sub-section were expected to remain unchanged in the final iteration of the 𝑆𝑇𝐼 vs. 𝐷𝐿2 model. 2.1.1.1 Speech Effort Spectrum The speech effort spectra used for calculating the speech sound pressure level at all distances were obtained from ANSI S3.5-1997 “Methods for Calculation of the Speech Intelligibility Index”. Speech spectra for Normal, Raised, and Loud vocal effort are shown in Table 2.1. These spectra are averages of male and female talkers, at 1 m directly in front of a talker’s mouth. 14 Table 2.1 - Speech Pressure Level (𝑳𝒑,𝒔,𝟏𝒎,𝟎°) Spectrum for Male and Female Talkers at 1 m Directly in Front of a Human Talker's Mouth (From ANSI S3.5-1997 “Methods for Calculation of the Speech Intelligibilty Index” [12]) Band [Hz] 125 250 500 1,000 2,000 4,000 8,000 Normal [dB] 54 57 60 54 49 44 39 Raised [dB] 62 61 66 62 57 51 43 Loud [dB] 70 64 70 71 66 60 49 Shout [dB] 78 65 75 80 76 69 58 2.1.2 Tentative Model Components The following components of the model were assumed and were intended to be adjusted based on experimental observations. 2.1.2.1 Speech Transmission Index (𝑆𝑇𝐼) The reverberant-speech Modulation Transfer Function-based (MTF) 𝑆𝑇𝐼 approximation method formulated by Houtgast et. al. was applied in the initial model. The MTF method calculates 𝑆𝑇𝐼 based solely on degradation of signal quality due to background noise and reverberation time. As full calculation details are described in publication [1], a summary of the method will be provided instead. Two forms of the 𝑆𝑇𝐼 approximation method were presented in the publication: (1) an reverberant speech 𝑆𝑇𝐼 model, and (2) a direct and indirect speech (complete) 𝑆𝑇𝐼 model. The reverberant speech 𝑆𝑇𝐼 model requires the background noise level and reverberation time whereas the complete 𝑆𝑇𝐼 model requires the room volume as well. As the room volume was not yet included in the model, the reverberant speech 𝑆𝑇𝐼 model (Eq. (2.1)) was used. For the reverberant speech model to be accurate, the total sound at the receiver needs to be comprised mainly of indirect sound. This requires that either (1) the distance be sufficiently large enough such that the direct sound field is negligible, or (2) there are obstructions between the talker and the listener. This is mostly applicable to open plan offices, where (1) workspace dividers are expected to obstruct the direct sound from reaching nearby listeners, or (2) the listener is located far away. 15 𝑚(𝑓) = [1 + (2𝜋𝑓𝑇13.8)]−1/2[1 + 10((−𝑆/𝑁)/10)]−1 (2.1) Where: 𝑚(𝑓) is the modulation transfer function for a given modulation frequency 𝑓 is the modulation frequency (from 0.4 – 30 Hz at third octave intervals) 𝑇 is the reverberation time (assumed to be 𝑇20) 𝑆/𝑁 is the signal to noise ratio Eq. (2.1) is evaluated at 18 modulation frequencies between 0.4 and 20 Hz at third octave intervals. The apparent signal to noise ratio (𝑆/𝑁𝑎𝑝𝑝) for each modulation frequency is then evaluated using Eq. (2.2). The 𝑆/𝑁𝑎𝑝𝑝 is then truncated at -15 dB if it is below -15 dB or truncated at +15 dB if it exceeds 15 dB. The 18 values for 𝑆/𝑁𝑎𝑝𝑝 are then averaged and normalized according to Eq. (2.3) to yield the 𝑆𝑇𝐼 contribution for each frequency band. Each frequency band’s 𝑆𝑇𝐼 contribution is then multiplied with their band weighting function for their contribution to intelligibility and summed to yield 𝑆𝑇𝐼. The band weightings are shown in Table 2.2. 𝑆/𝑁𝑎𝑝𝑝,𝐹 = 10 𝑙𝑜𝑔 (𝑚(𝐹)1 − 𝑚(𝐹)) (2.2) 𝑆𝑇𝐼𝑓 =118∑( 𝑆/𝑁𝑎𝑝𝑝) − 1530 (2.3) Table 2.2 - Octave Band 𝑺𝑻𝑰 Contributions [1] Frequency [Hz] 125 250 500 1000 2000 4000 8000 Weighting 0.13 0.14 0.11 0.12 0.19 0.17 0.14 16 2.1.2.2 Directionally Averaged Speech Power Spectrum Input for MTF In the complete 𝑆𝑇𝐼 model, the sound power level of the source is multiplied by human directivity factors for the direct field 𝑆𝑇𝐼 contribution. In the reverberant speech model, average sound power level was postulated to be required. This assumption was based on the idea that sound from a directive source would reflect off local surfaces, and the indirect sound reaching a listener would be averaged by this mechanism. The average speech pressure levels (𝐿𝑝,𝑠,1𝑚,𝑎𝑣𝑔) were calculated using the spectral human speech data from Table 2.1 and human-directivity data in Table 2.3 [13]. Source directivity (evaluated at angle 𝜃) is the ratio between the pressure-squared value for a sound source at angle 𝜃 and the average pressure-squared value for the source over 360° (Eq. (2.4)). Taking the logarithm and multiplying both sides of Eq. (2.4) by 10 yields the conversion between Lp,s,1m,0° and Lp,s,1m,avg (Eq. (2.5)). Calculated values for 𝐿𝑝,𝑠,1𝑚,𝑎𝑣𝑔 are shown in Table 2.4. Table 2.3 - Octave Band Human Directivity Data (From R. Watson, O. Downey “The Little Red Book of Acoustics: A Practical Guide”, 2008 [13]) Band [Hz] 125 250 500 1,000 2,000 4,000 8,000 Directivity 1.4 1.7 1.5 1.5 2.1 2.5 3.3 Table 2.4 - Speech Sound Pressure Level (𝑳𝒑,𝒔,𝟏𝒎,𝒂𝒗𝒈) Spectrum for Male and Female Talkers at 1 m, Averaged over 360° Band [Hz] 125 250 500 1,000 2,000 4,000 8,000 Normal [dB] 64 66 69 63 57 51 44 Raised [dB] 72 70 75 72 65 58 48 Loud [dB] 80 73 80 80 74 67 55 Shout [dB] 87 74 84 89 84 76 64 17 𝑄𝜃 =𝑃𝜃2𝑃𝑎𝑣𝑔2 (2.4) 𝐿𝑝,𝑎𝑣𝑔 = 𝐿𝑝,0° − 10 𝑙𝑜𝑔(𝑄𝜃) (2.5) 2.1.2.3 Background Noise Spectrum (𝐿𝑛) In rooms where music is not played over a speaker system, the main source of background noise was expected to be from mechanical services such as HVAC systems. As such, the spectrum of the background noise was assumed to be identical to the Balanced Noise Criterion (NCB) contours proposed by Beranek [14]. The NCB contours are updated versions of the Noise Criterion (NC) contours, which were used to evaluate HVAC systems. The NC contours were based on equal loudness contours, but were not described to describe occupied rooms, a shortcoming addressed by the NCB contours. For the idealized iteration of the model, NCB contours whose A-weighted sum equals the lowest or highest recommended background noise level in a given type of room were used. 2.1.2.4 Reverberation Time (RT) 𝐷𝐿2 was assumed to be independent of reverberation time, and the reverberation time was assumed to be the same at all frequencies. While Keranen’s empirical model stated that 𝐷𝐿2 is dependent on absorption [11], which directly affects reverberation time, 𝐷𝐿2 also depends on other factors such as furnishing and room geometry. This assumption was based on the expectation that 𝐷𝐿2 can be modified independent of reverberation time. While reverberation time is known to be frequency-dependent, the above assumption greatly simplifies the construction of the model. 2.1.2.5 Sound Pressure Level at 1m (𝐿𝑝,1𝑚) Sound pressure level at 1 m in rooms is often assumed to be equal to free-field levels; the sound pressure level at 1m in a room is the same as it would be in a free field. The free-field distance is defined as the distance at which sound pressure level is equal to that of the same source in a free-field environment. Hodgson’s findings for free-field distances in industrial rooms are shown in 18 Table 2.5. While general rooms may have higher furnishing density and more nearby surface than industrial rooms, Lp,1m was tentatively assumed to be equal to free-field values for point sources. Table 2.5 - Average and Standard Deviation (in Parentheses) for Free-Field Distances in Octave Bands for Empty, Fitted, and Fitted and Absorbent Industrial Rooms (From M. Hodgson, N. Heerema “Sound-Propagation Curves in Industrial Workrooms: Statistical Trends and Empirical Prediction Models” Building Acoustics, Vol. 3, 1996 [5]) Band [Hz] Empty Room [m] Fitted Room [m] Fitted + Absorbent [m] 125 1.07 (0.17) 0.92 (0.06) 0.90 (0.03) 250 1.04 (0.12) 0.88 (0.06) 0.89 (0.03) 500 1.05 (0.14) 0.86 (0.04) 0.88 (0.01) 1000 1.01 (0.09) 0.79 (0.04) 0.80 (0.02) 2000 1.04 (0.13) 0.87 (0.05) 0.90 (0.08) 4000 1.03 (0.15) 0.91 (0.03) 0.93 (0.08) 2.1.2.6 Uniform, Broadband Decay 𝐷𝐿2 was tentatively assumed to be frequency independent. That is, the value of 𝐷𝐿2 for all octave bands was assumed to be the same. As the 𝐷𝐿2 value of each octave band was assumed to be identical, the 𝐷𝐿2 value for the A-weighted speech sound pressure level would be the same as well. This assumption facilitates presentation of 𝐷𝐿2 as a single value. 2.1.2.7 Linear Decay Ondet and Hodgson observed that the 𝐷𝐿2 in smaller industrial rooms may be modeled with reasonable accuracy with a straight line up until 30 m [5] [7]. As unamplified speech is not expected to reach beyond 30 m, a linear decay is assumed to be applicable. 2.1.3 Construction of DL2 Model The 𝐷𝐿2 model was constructed in Microsoft Excel. The spreadsheet is divided into 4 main sections: a data entry/user interface sheet, a chart output sheet, 𝑀𝑇𝐹 calculation sheets (one sheet for each data point), and a common data sheet. The vocal speech effort levels and their corresponding spectra were added to a common data tab of the spreadsheet. The spectra are called upon using a drop-down menu on the data entry/user 19 interface sheet. The user selects a speech vocal effort level, and inputs the background noise spectrum, reverberation time spectrum, and 𝐷𝐿2 value (See Figure 2.1). The spreadsheet then uses the vocal speech effort levels to calculate the sound pressure level at the 1 m location. The spreadsheet then, calculates the sound pressure level at each doubling of distance. Figure 2.1 - Screenshot of Data Entry sheet of DL2 calculation tool The speech pressure level data in each row is then referenced in their respective 𝑀𝑇𝐹 calculation sheets (i.e. Position 1 is referenced in sheet P1, Position 2 is referenced in sheet P2). Each calculation sheet then evaluates the modulation transfer function according to Eq. (2.1) through (2.3). The 𝑀𝑇𝐹 is evaluated for each octave band at each modulation frequency. The spreadsheet then calculates the apparent signal to noise ratio, applies the band contribution weighting for each average apparent signal to noise ratio, then calculates the STI using three different speech weighting functions. The main weighting function of interest is the one specified by Houtgast and Steeneken. A screenshot of a typical calculation sheet is shown in Figure 2.2. 20 The model was implemented in two forms: (1) a Fixed 𝐷𝐿2 model where 𝐷𝐿2 is fixed and the 𝑆𝑇𝐼 is calculated at incremental distances (𝑆𝑇𝐼 vs Distance), and (2) a Fixed Distance model where the evaluation distance is fixed and the 𝑆𝑇𝐼 is calculated at incrementing 𝐷𝐿2 values (𝑆𝑇𝐼 vs 𝐷𝐿2). In both models, speech effort level, background noise level, and reverberation time are chosen to approximate the application under investigation. The Fixed 𝐷𝐿2 model (1) calculates the octave-band sound pressure level at incrementing distances based on a chosen 𝐷𝐿2 value. The Fixed Distance (2) model calculates the sound pressure level at a fixed distance at incrementing 𝐷𝐿2 values. Figure 2.2 - Screenshot of 𝑴𝑻𝑭 Calculation sheet of 𝑫𝑳𝟐 calculation tool 2.1.4 Sample Model Plots As the model is based on the indirect speech 𝑆𝑇𝐼 calculation scheme, the following sample plots represent environments where the direct sound is absent. Figures 2.3 and 2.4 were generated for a speaker at normal vocal effort in a room of broadband reverberation time = 0.3 s and 21 background noise spectrum equal to NCB contour 20 (approximately equal to 29 dBA). These room conditions approximate an open-plan office. Figure 2.3 is the 𝑆𝑇𝐼 vs Distance curve for 𝐷𝐿2 = 6 dB/DD. 𝑆𝑇𝐼 vs Distance curves are useful for post-occupancy evaluation of how 𝑆𝑇𝐼 varies between a talker and listeners at varying distances. The 𝐷𝐿2 measured is to be entered into this model along with an expected speech effort level to examine how STI decays as a function of distance. Alternatively, for rooms where speech intelligibility is desired throughout a room, this plot would help determine the maximum seating distance from a talker. This information is valuable for optimizing the seating arrangement such that listening effort is not an issue. Figure 2.3 - Sample STI vs Distance Curve Evaluated at DL2 = 6 dB/DD Figure 2.4 is the 𝑆𝑇𝐼 vs 𝐷𝐿2 curve for a listener located 4 m from a talker. 𝑆𝑇𝐼 vs 𝐷𝐿2 curves are useful for design-phase decisions. By choosing the listener position of interest, designers can determine the 𝐷𝐿2 required to meet speech intelligibility or speech privacy targets. 22 According to IEC 60268-16, ‘Bad’ speech intelligibility is rated at 𝑆𝑇𝐼 0.3 or less. This translates to good speech privacy and is therefore desirable in settings where speech distraction is to be minimized. According to Figure 2.4, an 𝑆𝑇𝐼 rating of 0.3 can be achieved at a distance of 4 m if the 𝐷𝐿2 is greater than 14.5 dB/DD. In Virjonen’s work, the maximum observed 𝐷𝐿2 value was 11.9 dB/DD – indicating that privacy at 4 m from a talker is not a reasonable expectation. This would either suggest that designers should expect lower speech privacy at 4 m, or reconsider the intended purpose of the space. Alternatively, according to the ASHRAE HVAC Handbook, the recommended maximum background noise level in open plan offices is 45 dBA [15]. Raising the background noise level to a broadband level of 45 dBA will reduce the 𝐷𝐿2 requirement to 7 dB/DD if good speech privacy is desired at a distance of 4 m from a speaker. Figure 2.4 - Sample STI vs DL2 Curve Evaluated at Distance = 4 m 2.2 𝐷𝐿2 Rating Scheme Alternatives Like the work by Virjonen et. al., the development of requirements and rating criteria for 𝐷𝐿2 was based on speech-related metrics. 𝑆𝑇𝐼 was chosen as the metric of choice as it is widely used and is 23 well-studied. Additionally, many speech-related studies refer to STI. Using other metrics such as the Speech Intelligibility Index (𝑆𝐼𝐼) are also viable options. Translation between metrics is made possible via tools such as the Common Intelligibility Scale (𝐶𝐼𝑆). However, one problem persists when STI is the primary rating metric: it is unintuitive to lay users. 𝑆𝑇𝐼 quality ratings span large ranges of values, using nebulous terms such as Excellent Intelligibility, Good Intelligibility, and Poor Intelligibility. The ranges of 𝐷𝐿2 values spanned by each STI quality rating in Figure 2.4 were compiled in Table 2.6. Noticeable differences are expected even within a single 𝑆𝑇𝐼 quality rating. Thus, more detailed and intuitive rating schemes were researched. Table 2.6 - Sample 𝑺𝑻𝑰 Ranges and their Corresponding DL2 Values According to IEC 60268-16 𝑺𝑻𝑰 Range Intelligibility Rating 𝑫𝑳𝟐 Range [dB/DD] 1.00 – 0.75 Excellent 0 – 3 0.75 – 0.60 Good 3 – 9 0.60 – 0.45 Fair 9 – 12 0.45 – 0.30 Poor 12 – 15 0.30 – 0.00 Bad >15 2.2.1 Room Purpose All rooms were categorized into one of three cases: (1) intelligibility, (2) distraction, and (3) privacy. The measurement and rating methodology are identical in all cases, differing only in the 𝑆𝑇𝐼 rating scheme. In all cases, the transition distance (𝑟𝑡𝑟) was introduced. The transition distance is a user-defined distance where the designer intends for the 𝑆𝑇𝐼 rating designation to change, and is the proposed distance where intelligibility is to be evaluated. This metric will be explained on a case-by-case basis. 2.2.1.1 Case 1: Intelligibility The intelligibility case was defined as rooms where high speech intelligibility is desired throughout the space. Example applications are classrooms and auditoria. In this setting, a speech intelligibility percentage of 100% is required; all speech must be audible. The rating brackets for the 24 intelligibility case are then based on listening effort. Then, 𝑟𝑡𝑟 is the farthest listener position from a talker as it represents the location where maximum listening effort is required. The rating criterion for this case is based on Rennies et. al.’s listening tests evaluating listening effort as a function of STI [16]. 16 normal-hearing German speakers were given 120 sample sentences at STI = 0.17, 0.30, 0.43, 0.50, 0.57, and 0.70. Each 𝑆𝑇𝐼 value was tested using different combinations of reverberation time and signal to noise ratio as it was postulated that the listening effort would be identical since intelligibility is theoretically linked to listening effort. Listeners were asked to report an effort between 1 to 11: 1 – very little effort, 3 – little effort, 5 – moderate effort, 7 – considerable effort, 9 – much effort, 11 – extreme effort. Figure 2.5 - Listening Effort vs. STI for 16 Normal-Hearing German Subjects for 120 German Sentences (Copied from J. Rennies and H. Schepker, "Listening Effort and Speech Intelligibility in Listening Situations Affected by Noise and Reverberation," Journal of the Acoustical Society of America, vol. 136, no. 5, pp. 2642-2653, 2014.) Figure 2.5 shows the listening effort and percentage of speech intelligibility as a function of STI. This figure was copied from J. Rennies and H. Schepker’s publication "Listening Effort and Speech 25 Intelligibility in Listening Situations Affected by Noise and Reverberation," published in volume 136 of the Journal of the Acoustical Society of America in 2014. Condition 1 (𝑇60 = 0) results were omitted as all rooms are expected to have non-zero reverberation times. In Condition 4, the test speech signal was generated by convolving a clean speech signal with different Room Impulse Response (𝑅𝐼𝑅). 𝑅𝐼𝑅𝑤𝑛 was a room impulse response generated using white noise, 𝑅𝐼𝑅𝑟𝑒𝑎𝑙 used 𝑅𝐼𝑅 taken from real rooms, and 𝑅𝐼𝑅𝑠𝑖𝑚 used simulated 𝑅𝐼𝑅. 𝑆𝑇𝐼 thresholds in Table 2.7 were chosen based on the maximum effort between the three 𝑅𝐼𝑅 condition results. Table 2.7 - Quality Ratings for STI Based on Listening Effort [16] Effort Rating Listening Effort STI Range Intelligibility [%] Acceptable Rating 1 Very little effort 0.73 – 1.00 100 Yes Excellent 3 Little effort 0.62 – 0.73 100 Yes Good 5 Moderate effort 0.53 – 0.62 100 Yes Poor 7 Considerable effort 0.43 – 0.53 100 Yes Bad 9 Much effort 0.35 – 0.43 88 No N/A 11 Extreme effort 0.30 – 0.35 80 No N/A 2.2.1.2 Case 2: Distraction The distraction case encompasses rooms where concentration on tasks is the main purpose, such as study spaces or open-plan offices. The rating criterion for this case is based on the notion that semantic speech is detrimental to serial memory and concentration. In the distraction case, 𝑟𝑡𝑟 is the distance to the nearest seat in rooms such as libraries or study halls, or to the nearest workspace in rooms such as open plan offices. Hongisto conducted a literature review on performance versus 𝑆𝑇𝐼 tests under the postulation that loss of productivity is a function of 𝑆𝑇𝐼 [17]. The results between silence and when 𝑆𝑇𝐼 was greater than 0 were compiled and are shown in Figure 2.6, this figure was copied from Hongisto’s publication "A Model for Predicting the Effect of Speech of Varying Intelligibility on Work Performance," published in volume 15 of Indoor Air in 2005 [17]. The prediction model used a Boltzmann’s sigmoidal function, and is an approximation of a wide variety of speech signals, 26 including normal speech in the participant’s native language, normal speech in a foreign language, incoherent words and reversed speech. Ebissou et. al. evaluated Hongisto’s model with a serial memory task at 𝑆𝑇𝐼 values of 0.25, 0.35, 0.45, and 0.65 [18]. Subjects were either unaffected, as they found the task easy, or were severely affected. A sharp decrease in productivity was also observed between 𝑆𝑇𝐼 = 0.35 – 0.45, but the maximum distraction occurred much sooner at 0.45. This thesis assumes that the tasks conducted in typical work or study environments are difficult and that most people will be affected adversely. Figure 2.6 - Compiled Data and Prediction Model for Loss of Productivity (𝑫𝑷) vs 𝑺𝑻𝑰 (Copied from V. Hongisto, "A Model for Predicting the Effect of Speech of Varying Intelligibility on Work Performance," Indoor Air, vol. 15, pp. 458-468, 2005 [17]) Quality rating brackets were assigned by subdividing the range between 0 – 7% loss in productivity (𝐷𝑃). This corresponds to an 𝑆𝑇𝐼 range of between 0.2 – 0.6. DP exceeding 7% (𝑆𝑇𝐼 > 0.6) was deemed unacceptable, while DP at 0% (𝑆𝑇𝐼 < 0.2) was deemed excellent. Table 2.8 shows the proposed quality ratings and their associated 𝑆𝑇𝐼 ranges if Hongisto’s prediction model were 27 subdivided into equal percentages of distraction. Note that the steep increase in the loss of productivity between 𝑆𝑇𝐼 = 0.35 – 0.50 leads to narrower 𝑆𝑇𝐼 ranges for Fair and Poor ratings. It should be noted that, since the prediction curve was based on a variety of speech types across different experiments, the curve presented in Figure 2.6 shows the minimum expected loss of productivity for any speech distraction. Intelligible conversations are therefore expected to result in even greater degrees of productivity loss. However, the form of the loss of productivity curve is expected to be an accurate representation regardless of the type of speech. The region between 𝑆𝑇𝐼 = 0.2 – 0.6 is still expected to be where loss of productivity transitions from 0% to its steady maximum. Table 2.8 - Proposed Quality Ratings for Speech-Related Productivity Loss Rating Loss of Productivity [%] 𝑺𝑻𝑰 Excellent 0 0.00 – 0.20 Good 0 – 2 0.20 – 0.35 Fair 2 – 4 0.35 – 0.43 Poor 4 – 6 0.43 – 0.50 Bad 6 – 7 0.50 – 0.60 Unacceptable > 7 > 0.60 2.2.1.3 Case 3: Privacy The privacy case refers to situations where reasonable intelligibility is expected at an intended recipient and privacy is expected at the next nearest listener. In rooms such as eating establishments and reception areas, the intended recipient should be able to understand the talker with little to no effort (𝑆𝑇𝐼 greater than 0.62 according to Table 2.7), and should have less than 100% speech intelligibility at the next nearest listener. In this case, the 𝑟𝑡𝑟 is the distance to the nearest listener where privacy is desired. However, the 𝑆𝑇𝐼 at the intended listener must also be checked to ensure that the intelligibility is sufficiently high (𝑆𝑇𝐼 > 0.62). Table 2.9 shows the quality ratings and their corresponding 𝑆𝑇𝐼 values derived from Figure 2.5. 28 Table 2.9 - Proposed Quality Ratings for Speech Privacy Rating Percentage of Intelligible Speech [%] 𝑺𝑻𝑰 Excellent < 50 < 0.15 Good 50 – 60 0.15 – 0.20 Fair 60 – 80 0.20 – 0.27 Poor 80 – 90 0.27 – 0.35 Bad 90 – 100 0.36 – 0.43 Unacceptable > 100 > 0.43 2.3 Conclusion An ideal, preliminary 𝐷𝐿2 model was developed using Houtgast and Steeneken’s reverberant speech 𝑆𝑇𝐼 calculation method (Eq. (2.1)) to establish a base for improving with experimental data. The model uses standardized speech spectra provided by ANSI S3.5 1997. The speech pressure level at 1 m was assumed to be equal to levels expected according to free-field sound decay for a point source. 𝐷𝐿2 was then assumed to be frequency-independent and constant as a function of distance. Reverberation time was assumed to be frequency independent while the background noise level in rooms was assumed to be accurately approximated using the Balanced Noise Criterion curves. The model calculates the speech sound pressure level at distance intervals that increase by a factor of 2 and calculates the 𝑆𝑇𝐼 at each position. The model was used to produce two different visual presentations of 𝐷𝐿2. The first presents 𝑆𝑇𝐼 as a function of distance for a given 𝐷𝐿2 value. The second presents 𝑆𝑇𝐼 as a function of 𝐷𝐿2 for a given distance. These two visual presentations are expected to give full insight to the acoustical performance of a room. Acoustical quality rating schemes were formulated by assuming all rooms are classifiable under one of three categories: good speech intelligibility desired throughout the room (Case 1, intelligibility); good speech intelligibility desired until a certain point, beyond which, low speech intelligibility is desired to reduce speech distraction (Case 2, distraction); and good speech 29 intelligibility desired until a certain point, beyond which, high speech privacy is desired for confidentiality reasons (Case 3, privacy). 30 3 Experimental Verification In the chapter 2, an idealized model for 𝐷𝐿2 was introduced. This chapter uses data collected in existing rooms to assess the assumptions employed in the idealized 𝐷𝐿2 model such that it can be improved to better reflect the behavior of sound in real rooms. 3.1 𝐷𝐿2 in Real Rooms This chapter investigates three assumptions made in Chapter 2 and is therefore divided into three subsections. Since the three subsections are different analyses of the same data set, they share a common methodology section. Each subsection is then divided into its own Measurement Results, Discussion and Conclusions sections. 3.1.1 Motivation The main objective of using 𝐷𝐿2 measurements was to re-evaluate three assumptions made in Chapter 2. The first assumption, uniform, broadband decay (Chapter 2.1.2.6) assumed that 𝐷𝐿2 is frequency independent, and that all octave bands and the A-weighted speech pressure level decay at the same rate. The second assumption, linear decay (Chapter 2.1.2.7) assumed that a 𝐷𝐿2 is constant and does not change with distance from the source. The third assumption, sound pressure levels at 1 m, 𝐿𝑝,1𝑚 (Chapter 2.1.2.6), assumed that the sound pressure at 1 m from a source in a room is identical to that of a free-field environment. As surface absorption and reverberation time are frequency dependent, 𝐷𝐿2 is also expected to vary with frequency (i.e. the assumption of uniform, broadband decay may not hold true). As such, experimental data was necessary to either confirm the applicability of assuming that 𝐷𝐿2 is acceptably uniform from 125 – 8,000 Hz or refine the model with any observable trends. The data was also used to assess the suitability of DL2 applied to the A-weighted speech pressure level (𝐷𝐿2,𝑠,𝐴) as a representative quantity. The assumption of linear decay was reassessed since a single room has been observed to have two different values for 𝐷𝐿2 (i.e. a change in slope): a lower rate of sound decay at small distances, and a higher rate of sound decay at larger distances. However, this behavior is mostly documented in open-plan offices and industrial rooms, which span large measurement distances in highly 31 furnished environments. Measurements in other types of rooms and at shorter distances are lacking, other than Hodgson’s measurements in classrooms [8], whose data suggests that a single 𝐷𝐿2 value may be sufficient in describing a room. As 𝐷𝐿2 was proposed as a universal room acoustics parameter, its measurement methodology should be consistent regardless of room type or rating scheme. The three rating schemes proposed in chapter 2.2 assumed the presence of an intended listener at short distance (e.g. in the same workstation of an open-plan office, or across an eating establishment table). As such, 𝐷𝐿2 measurements should start at a distance of 1 m from the source. The maximum recommended distance for measuring 𝐷𝐿2 should yield a regression that approximates actual spatial decay behavior with reasonable accuracy regardless of room type. It was therefore of interest to examine the behavior of 𝐷𝐿2 in a wide variety of rooms to confirm the maximum distance until which a single value of 𝐷𝐿2 is sufficiently accurate. The assumption that the sound pressure level in rooms at 1 m is equal to that of point-source decay in a free-field environment was based on Hodgson’s observation for the free field distance in industrial rooms [5]. However, this assumption may only hold true for rooms where acoustically reflective surfaces or objects are located far from a source. When fittings were introduced in empty industrial rooms, the free-field distance decreased from 1.01 – 1.07 m to 0.79 – 0.92 m. Calculating 𝑆𝑇𝐼 normally requires the sound power level of the source be known, but loudspeaker calibrations may change over time. Thus, measurements within the free-field distance are commonly used as field calibration checks since anechoic loudspeaker calibrations are time and labour intensive. However, the free-field distance being from 0.72 – 0.92 m for fitted industrial rooms suggests that using 𝐿𝑝,1𝑚 data for field calibrations is insufficient. As such, comparing 𝐿𝑝,1𝑚 to its expected free-field decay for point sources was of interest. 3.1.2 Methodology Analysis was performed on existing 𝐷𝐿2 data collected from a post-occupancy evaluation in 21 healthcare office buildings, and data collected from a separate acoustical study of the Macmillan building on UBC’s Vancouver campus. In total, 62 𝐷𝐿2 measurements from 22 buildings were used. For each 𝐷𝐿2 dataset, background noise level, reverberation time, and sound pressure level versus distance was measured. 32 An Acer Aspire 5100 laptop equipped with WinMLS 2004 room acoustics software was used to measure the room’s impulse response, which was then used to calculate reverberation time. To measure the reverberation time, WinMLS was used to generate a Maximum Length Sequence (MLS) signal. The signal was amplified through a QSC USA 370 power amplifier and played through a dodecahedral loudspeaker array. The skewed MLS was then detected using a Rion NA-28 sound level meter functioning as an audio capture microphone, where the signal was routed to the laptop’s line-in input for data acquisition. The signal chain is illustrated in Figure 3.1. Figure 3.1 - Diagram showing signal chain for measuring reverberation time Reverberation time was measured 3 – 5 times at different loudspeaker-microphone pair locations in each room depending on the room size. More reverberation time measurements were taken in larger rooms such as open-plan offices, and less in smaller rooms such as meeting rooms. 𝑇20 reverberation times were used, and the measurements were averaged in each octave band from 125 – 8,000 Hz. The same equipment was used to measure the steady-state sound pressure level (𝐿𝑝). Here, the Rion NA-28 was used as a sound level meter instead of an audio capture microphone. For ease of setup repeatability, the laptop and power amplifiers were set to their maximum output levels. WinMLS was used to generate a constant MLS signal as it is spectrally similar to white noise, which has the same energy at all frequencies. 33 The signal chain was calibrated for output sound power level in an anechoic chamber. The sound level meter was used to measure the dodecahedral array 40 times at 1 m. Each sound pressure level measurement was converted to its pressure-squared quantity using Eq. (1.1), then averaged. The resulting average pressure-squared quantity was converted back to sound pressure level to calculate the sound power level using Eq. (1.5). For each DL2 measurement, the dodecahedral array was positioned at a height of 1.2 m to simulate a seated talker and was placed at least 1 m away from any nearby surfaces to avoid the Waterhouse Effect. The Waterhouse Effect accounts for sound reflection (and then direct wave superimposition), stating that each surface within 1/4 wavelengths of a source doubles the source’s directivity factor, resulting in an additional 3 dB per nearby orthogonal surface. The lowest frequency band measured was 125 Hz, which corresponds to a quarter-wavelength of 0.69 m. The sound level meter was then used to measure the sound pressure level at a height of 1.2 m, at intervals of doubling distance, starting at 1 m (1, 2, 4, 8, 16, … m). In cases where measurements were not possible at the exact distance, the nearest possible measurement location was used, and the measurement distance was documented. A typical measurement setup is illustrated in Figure 3.2. Figure 3.2 - Diagram showing the typical measurement setup All raw sound pressure level data are provided in Appendix . The data provided are the distance, the sound pressure level as measured from the dodecahedral loudspeaker array, and the A-weighted speech pressure level for normal vocal effort. The following naming convention was 34 used: building number – room number – measurement number. For example: B-22-3 and B-22-4 would be rooms 3 and 4 in building 22, then B-22-4-1 and B-22-4-2 would be measurements 1 and 2 in room 4. Multiple measurements in one room were mostly taken in building 22. 3.1.3 Uniform, Broadband Decay 𝐷𝐿2 measurements were divided into ones made in standard rooms and ones made in open-plan offices. Rooms where the airspace was continuous were referred to as standard rooms. Open-plan offices were defined by the presence of workspace dividers. 3.1.3.1 Measurement Results For each measurement, 𝐷𝐿2 was calculated over the full range of data in each octave band (𝐷𝐿2,𝑓) and the A-weighted speech pressure level (𝐷𝐿2,𝑠,𝐴). The average 𝐷𝐿2 values are shown in Table 3.1. The difference between 𝐷𝐿2,𝑓 and 𝐷𝐿2,𝑠,𝐴 was also calculated, and the averages are shown in Table 3.2. Overall averages using all measurement data were excluded as most of the data was taken in open-plan offices. This would skew the averages in favor of behavior in open-plan offices. Table 3.1 - Average 𝑫𝑳𝟐,𝒇 and 𝑫𝑳𝟐,𝒔,𝑨 for (1) Open-plan Offices and (2) Standard Rooms in dB/DD. Open-plan Offices Frequency [Hz] 125 250 500 1000 2000 4000 8000 𝑳𝒑,𝒔,𝑨 Average [dB/DD] 4.7 6.5 7.4 8.1 7.9 7.6 7.9 7.2 St. Dev [dB/DD] 1.1 1.4 1.6 1.8 1.8 1.9 2.1 1.4 Standard Rooms Frequency [Hz] 125 250 500 1000 2000 4000 8000 𝑳𝒑,𝒔,𝑨 Average [dB/DD] 3.1 3.1 3.3 3.2 3.2 3.5 4.2 3.2 St. Dev [dB/DD] 1.3 1.4 1.3 1.2 1.3 1.1 1.1 1.3 35 Table 3.2 - Average Difference between 𝑫𝑳𝟐,𝒇 and 𝑫𝑳𝟐,𝒔,𝑨 for (1) Open-plan Offices and (2) Standard Rooms in dB/DD. Open-plan Offices Frequency [Hz] 125 250 500 1000 2000 4000 8000 Average [dB/DD] -2.5 -0.7 0.1 0.9 0.7 0.4 0.7 St. dev. [dB/DD] 1.4 0.7 0.3 0.6 0.8 0.9 1.0 Standard Rooms Frequency [Hz] 125 250 500 1000 2000 4000 8000 Average [dB/DD] -0.1 -0.1 0.1 0.0 -0.1 0.2 0.9 St. dev. [dB/DD] 0.9 0.5 0.2 0.2 0.3 0.5 0.8 3.1.3.2 Discussion The standard deviation ranged from 0.3 – 1.4 dB/DD in open-plan offices and 0.2 – 0.9 dB/DD in standard rooms. By comparing the averages to the individual measurement data (which contained both positive and negative values in all bands), it was apparent that a simple arithmetic averaging produced misleadingly low differences between 𝐷𝐿2,𝑓 and 𝐷𝐿2,𝑠,𝐴. The absolute difference between 𝐷𝐿2,𝑓 and 𝐷𝐿2,𝑠,𝐴 was also computed, and is shown in Table 3.3. As expected, the average difference increased while standard deviation decreased. The absolute differences were then used to assess the sensitivities of 𝐷𝐿2,𝑠,𝐴 and 𝑆𝑇𝐼 to deviations in individual octave bands. Table 3.3 - Average Absolute Difference for 𝑫𝑳𝟐,𝒇 – 𝑫𝑳𝟐,𝒔,𝑨for (1) Open-plan Offices and (2) Standard Rooms. Open-plan Offices Frequency [Hz] 125 250 500 1000 2000 4000 8000 Average [dB/DD] 2.5 0.8 0.2 0.9 0.8 0.7 1.0 St. dev. [dB/DD] 1.4 0.5 0.2 0.6 0.6 0.6 0.7 Standard Rooms Frequency [Hz] 125 250 500 1000 2000 4000 8000 Average [dB/DD] 0.7 0.4 0.1 0.2 0.3 0.4 1.0 St. dev. [dB/DD] 0.5 0.3 0.1 0.2 0.2 0.4 0.7 36 Open-plan Offices For open plan offices, the greatest difference between 𝐷𝐿2,𝑓 and 𝐷𝐿2,𝑠,𝐴 occurred in the 125 Hz band, with 𝐷𝐿2,125𝐻𝑧 being typically 2.5 dB/DD lower than that of 𝐷𝐿2,𝑠,𝐴. This difference may be attributed to acoustical treatment in rooms being less effective at lower frequencies. Additionally, low frequencies exhibit more refraction than high frequencies. This is evident as the 𝐷𝐿2 values were lowest at 125 Hz and increased with increasing frequency up to 500 Hz. As the A-weighting for the 125, 250, and 500 Hz bands are -16.1 dB, -8.6 dB, and -3.2 dB respectively, these bands were expected to influence the A-weighted speech pressure level less than the 1,000, 2,000, 4,000, and 8,000 Hz bands whose adjustments are 0 dB, +1.2 dB, +1.0 dB, and -1.1 dB. DL2 for the octave bands from 500 to 8,000 Hz was higher that 𝐷𝐿2,𝑠,𝐴, ranging from 0.2 – 1.0 dB/DD. 𝐷𝐿2,500𝐻𝑧 was closest to 𝐷𝐿2,𝑠,𝐴 at an average value of 0.2 dB/DD and a standard deviation of 0.2 dB/DD, suggesting its usefulness as an approximation to 𝐷𝐿2,𝑠,𝐴. Standard Rooms The octave bands with the greatest deviation from 𝐷𝐿2,𝑠,𝐴 were the 125 Hz band at -0.7 dB/DD and the 8,000 Hz band at 1.0 dB/DD. The deviation in the 125 Hz band was due to standard room furnishing being not thick enough to absorb energy at lower frequencies. Conversely, standard acoustic treatment is expected to absorb sound energy at 8,000 Hz most effectively, resulting in a higher 𝐷𝐿2 value. The 500, 1,000 and 2,000 and 4,000 Hz bands are close to 𝐷𝐿2,𝑠,𝐴 because they are largely unaffected by the A-weighting and thus contribute the most energy to the human speech spectrum. Deviations in 125 Hz affect 𝐷𝐿2,𝑠,𝐴 less due to the 16.1 dB penalty from the A-weighting. 𝑫𝑳𝟐,𝒔,𝑨 Sensitivity A sensitivity analysis was conducted using the model developed in Chapter 2. The changes in 𝐷𝐿2,𝑠,𝐴 due to frequency-dependent deviations were observed by varying the 𝐷𝐿2 value of 37 individual bands by +/- 1 dB/DD. The largest deviations shown in Table 3.3 were also assessed. The results are shown in Table 3.4. Table 3.4 - 𝑫𝑳𝟐,𝒔,𝑨 Sensitivity to Deviations in Individual Octave Bands. FREQUENCY [Hz] 125 250 500 1000 2000 4000 8000 +1 dB/DD [dB/DD] +0.001 +0.065 +0.449 +0.123 +0.048 +0.011 +0.002 -1 dB/DD [dB/DD] -0.004 -0.181 -0.718 -0.306 -0.137 -0.036 -0.006 Table 3.3 [dB/DD] -0.031 -0.130 +0.113 +0.116 +0.042 +0.009 +0.002 𝐷𝐿2,𝑠,𝐴 was most sensitive to deviations in the 250 – 2,000 Hz octave bands, which lead to changes of between 0.2 – 0.8 dB/DD per dB/DD of deviation. 𝐷𝐿2,𝑠,𝐴 was significantly less sensitive to deviations in the 4,000 and 8,000 Hz bands, which lead to changes of between 0.01 – 0.07 dB/DD per dB/DD of deviation. Using the model developed in Chapter 2, the effects on STI were evaluated for the maximum deviations observed in the 4,000 and 8,000 Hz bands. At deviations of 2.0 dB/DD at 4,000 Hz and 2.3 dB/DD at 8,000 Hz, the total change in 𝐷𝐿2,𝑠,𝐴 was -0.162 dB/DD, but changes in STI were up to 0.07 points. Approximation of 𝑫𝑳𝟐,𝒇 Relative to 𝑫𝑳𝟐,𝒔,𝑨 The average values of 𝐷𝐿2,𝑓 suggest that uniform, broadband decay was an invalid assumption for open plan offices. While 𝐷𝐿2,𝑠,𝐴 is insensitive to deviations in the 125, 250, 4,000 and 8,000 Hz bands, STI is not. As such, using the average deviations from 𝐷𝐿2,𝑠,𝐴 shown in Table 3.2 to adjust 𝐷𝐿2,𝑓 relative to 𝐷𝐿2,𝑠,𝐴 may be used to better predict how STI varies with distance. In standard rooms, this assumption appeared to hold true as furnishing in standard rooms is rarely expected to obstruct the line of sight between a speaker and a receiver. For improved prediction accuracy, the adjustment values in Table 3.2 may be used. 38 3.1.3.3 Conclusion For each room, 𝐷𝐿2 was computed for the A-weighted speech pressure level and each octave band. The results were grouped into open-plan offices and standard rooms. The difference between 𝐷𝐿2,𝑠,𝐴 and 𝐷𝐿2,𝑓 were also computed to investigate how 𝐷𝐿2,𝑓 differs from 𝐷𝐿2,𝑠,𝐴. In open-plan offices, 𝐷𝐿2,500𝐻𝑧 was most similar to 𝐷𝐿2,𝑠,𝐴. The maximum deviations from 𝐷𝐿2,𝑠,𝐴 were -2.5 dB/DD in the 125 Hz band, and +1.0 dB/DD in the 8,000 Hz band. On average, relative to 𝐷𝐿2,𝑠,𝐴, 𝐷𝐿2,𝑓 was -2.5 dB/DD at 125 Hz, -0.8 dB/DD at 250 Hz, +0.2 dB/DD at 500 Hz, +0.9 dB/DD at 1,000 Hz, +0.8 dB/DD at 2,000 Hz, +0.7 dB/DD at 4,000 Hz, and +1.0 dB/DD at 8,000 Hz. In standard rooms, the difference between 𝐷𝐿2,𝑓 and 𝐷𝐿2,𝑠,𝐴 was small with the exception of 125 and 8,000 Hz band. On average, relative to 𝐷𝐿2,𝑠,𝐴, 𝐷𝐿2,𝑓 was -0.7 dB/DD at 125 Hz, -0.4 dB/DD at 250 Hz, +0.1 dB/DD at 500 Hz, +0.2 dB/DD at 1,000 Hz, +0.3 dB/DD at 2,000 Hz, +0.4 dB/DD at 4,000 Hz and +1.0 dB/DD at 8,000 Hz. Uniform, broadband decay was shown to be invalid for open plan offices. However, this assumption was reasonable for standard rooms without sub-dividers in the space. In the model, the octave-band DL2 values were adjusted using the average deviations shown in Table 3.2 for open plan offices, and adjustment values can be considered optional for standard rooms. 3.1.4 Linear Decay 3.1.4.1 Measurement results The A-weighted speech pressure level, 𝐿𝑝,𝑠,𝐴, was plotted versus distance for open plan offices and standard rooms in Figures 3.3 through 3.8. For open plan offices, the data was grouped based on workspace divider height (𝐻𝑑𝑖𝑣𝑖𝑑𝑒𝑟). 𝐷𝐿2 values were then calculated over two ranges: (1) from 1 – 16 m, 𝐷𝐿2,𝑠,𝐴,1−16𝑚 and (2) between distances of 4 m and the maximum room distance, in accordance with Keranen, 𝐷𝐿2,𝑠,𝐴,4𝑚 [10]. The values are shown in Table 3.5 and Figures 3.3 and 3.8. Measurements were grouped into open-plan offices and standard rooms. The open-plan office measurements were further divided based on workspace divider height. The following room types were classified as standard rooms: meeting rooms (MR), activity rooms (AR), classrooms (CR), acoustically untreated 39 computer labs (CL-U), acoustically treated computer labs (CL-T), empty lunch rooms (LR-E), and furnished lunch rooms (LR-T). Two base-2 logarithmic regressions were calculated for each room. The first regression was for data between the distances of 1 m and 16 m. A maximum distance of 16m was chosen as rooms rarely exceeded this length (𝐷𝐿2,𝑠,𝐴,1−16𝑚). The second regression was for the measurement range proposed by Keranen (𝐷𝐿2,𝑠,𝐴,4𝑚), which starts at 4 m and ends at the maximum possible distance in the space. The regressions were used to predict 𝐿𝑝,𝑆,𝐴 values at all measurement distances for each dataset. Prediction errors were then calculated for both regression models. The prediction error, 𝐸𝑒−𝑟, was defined as the error between measured A-weighted speech pressure level (𝐿𝑝,𝑆,𝐴,𝑒𝑥𝑝) and the A-weighted predicted speech pressure level (𝐿𝑝,𝑆,𝐴,𝑟𝑒𝑔). The prediction errors were compiled and are shown in Figures 3.9 through 3.14 for DL2 between 1 – 16 m (𝐷𝐿2,𝑠,𝐴,1−16𝑚), and Figures 3.15 through 3.20 for 𝐷𝐿2 between 4 m and the maximum distance in a room (𝐷𝐿2,𝑠,4𝑚). The averaged absolute prediction error and maximum prediction errors for each room are compiled in Tables 3.6 and 3.7. 40 Figure 3.3 - 𝑳𝒑,𝒔,𝑨,𝒆𝒙𝒑 vs Distance for Open-plan Offices (1.2 m < 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 < 1.3 m). Figure 3.4 - 𝑳𝒑,𝒔,𝑨,𝒆𝒙𝒑 vs Distance for Open-plan Offices (𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 = 1.4 m). 41 Figure 3.5 - 𝑳𝒑,𝒔,𝑨,𝒆𝒙𝒑 vs Distance for Open-plan Offices (𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 = 1.5 m). Figure 3.6 - 𝑳𝒑,𝒔,𝑨,𝒆𝒙𝒑 vs Distance for Open-plan Offices (1.6 m < 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 < 1.8 m). 42 Figure 3.7 - 𝑳𝒑,𝒔,𝑨,𝒆𝒙𝒑 vs Distance for Open-plan Offices (𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 > 2 m). Figure 3.8 - 𝑳𝒑,𝒔,𝑨,𝒆𝒙𝒑 vs Distance for Standard Rooms. 43 Table 3.5 - Measured DL2 Grouped by Room Type, then by Divider Height for Open-plan Offices. Open-plan Offices 1.2 - 1.3 m dividers (Figure 3.3) 1.4 m dividers (Figure 3.4) 1.5 m dividers (Figure 3.5) Room Hdivider DL2,11 DL2,21 Room Hdivider DL2,1 DL2,2 Room Hdivider DL2,1 DL2,2 B1-1 1.2 m 6.8 7.0 B9 1.4 m 6.4 7.8 B1-2 1.5 m 6.2 7.9 B2 1.2 m 5.9 8.1 B10-2 1.4 m 7.5 9.5 B4-1 1.5 m 7.5 10.3 B3-1 1.2 m 5.4 5.9 B18-2 1.4 m 7.7 8.9 B4-2 1.5 m 4.8 1.1 B3-2 1.2 m 7.3 8.6 B18-4 1.4 m 5.1 7.5 B5-1 1.5 m 6.4 8.2 B6-2 1.3 m 7.4 9.2 B18-5 1.4 m 5.7 4.9 B5-2 1.5 m 5.3 7.8 B8 1.2 m 8.8 8.3 B7-1 1.5 m 5.7 9.6 B13-2 1.2 m 8.3 13.8 B7-2 1.5 m 6.7 9.1 B16-1 1.3 m 7.9 10.0 B17-1 1.2 m 7.8 8.6 B17-3 1.2 m 7.0 8.2 B20-2 1.2 m 6.2 7.0 Open-plan Offices Standard Rooms 1.6 - 1.8 m dividers (Figure 3.6) > 2 m dividers (Figure 3.7) Standard rooms (Figure 3.8) Room Hdivider DL2,1 DL2,2 Room Hdivider DL2,1 DL2,2 Room Desc. DL2,1 DL2,2 B1-3 1.7 m 7.2 9.3 B10-3 2.4 m 4.3 6.0 B4-3 MR2 2.9 2.9 B6-1 1.7 m 8.6 8.3 B10-4 2.4 m 8.8 9.6 B20-1 LR2 3.0 3.0 B10-1 1.8 m 8.9 5.4 B18-1 2 m 7.0 9.2 B21-1 LR2 2.6 2.7 B11-1 1.7 m 8.8 9.6 B18-3 2 m 7.0 9.2 B21-2 AR2 3.1 2.9 B11-2 1.7 m 7.2 8.7 B22-3-1 2 m 5.0 5.7 B22-1 CR2 1.0 0.9 B12-1 1.7 m 9.1 8.8 B22-3-2 2 m 2.9 5.1 B22-2-1 CR2 1.1 N/A B12-2 1.7 m 9.1 9.2 B22-3-3 2 m 4.8 6.1 B22-2-2 CR2 1.4 0.8 B13-1 1.7 m 8.9 9.5 B22-4-1 CL-U2 1.8 1.7 B14-1 1.7 m 8.3 13.0 B22-4-2 CL-U2 2.1 1.8 B14-2 1.7 m 6.8 6.4 B22-4-3 CL-U2 3.2 0.1 B15-1 1.8 m 6.3 9.7 B22-4-4 CL-U2 2.1 1.7 B15-2 1.8 m 5.8 7.4 B22-5-1 CL-T2 4.8 4.2 B16-2 1.7 m 7.9 6.8 B22-5-2 CL-T2 2.7 N/A B17-2 1.7 m 7.3 6.4 B22-6-1 LR-E2 2.5 2.6 B17-4 1.7 m 6.8 9.1 B22-6-2 LR-T2 2.3 2.2 B19 1.7 m 8.3 10.9 1 - DL2,1 is for DL2 regression calculated between 1-16m (DL2,S,A,1-16m), DL2,2 is for DL2 regressions calculated from 4m and onwards (DL2,S,A,4m) 2 – MR = Meeting Room, LR = Lunch Room, AR = Activity Room, CR = Classroom, CL-U = Acoustically Untreated Computer Lab, CL-T = Acoustically Treated Computer Lab, LR-E = Empty Lunch Room, LR-T = Lunch Room with Tables 44 Figure 3.9 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝑺,𝑨,𝟏−𝟏𝟔𝒎 (Open-plan Offices, 1.2 m < 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 < 1.3 m). Figure 3.10 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝑺,𝑨,𝟏−𝟏𝟔𝒎 (Open-plan Offices, 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 = 1.4 m). 45 Figure 3.11 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝑺,𝑨,𝟏−𝟏𝟔𝒎 (Open-plan Offices, 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 = 1.5 m). Figure 3.12 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝑺,𝑨,𝟏−𝟏𝟔𝒎 (Open-plan Offices, 1.6 m < 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 < 1.8 m). 46 Figure 3.13 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝑺,𝑨,𝟏−𝟏𝟔𝒎 (Open-plan Offices, 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 > 2 m). Figure 3.14 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝑺,𝑨,𝟏−𝟏𝟔𝒎 (Standard Rooms). 47 Figure 3.15 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝒔,𝟒𝒎 (Open-plan Offices, 1.2 m < 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 < 1.3 m). Figure 3.16 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝒔,𝟒𝒎 (Open-plan Offices, 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 = 1.4 m). 48 Figure 3.17 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝒔,𝟒𝒎 (Open-plan Offices, 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 = 1.5 m). Figure 3.18 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝒔,𝟒𝒎 (Open-plan Offices, 1.6 m < 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 < 1.8 m). 49 Figure 3.19 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝒔,𝟒𝒎 (Open-plan Offices, 𝑯𝒅𝒊𝒗𝒊𝒅𝒆𝒓 > 2 m). Figure 3.20 - 𝑫𝑳𝟐 Regression Error for 𝑫𝑳𝟐,𝒔,𝟒𝒎 (Standard Rooms). 50 Table 3.6 - Average Absolute Regression Error Comparison Between Lp,S,A,1-16m and Lp,S,A,4m in dB. Open-plan Office (Figures 3.9 and 3.15) Open-plan Office (Figures 3.10 and 3.16) Open-plan Office (Figures 3.11 and 3.17) Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m B1-1 1.6 1.2 B9 0.9 0.3 B1-2 1.3 2.4 B2 0.7 0.5 B10-2 1.9 1.8 B4-1 1.7 0.6 B3-1 0.6 0.3 B18-2 0.5 0.2 B4-2 1.6 N/A B3-2 1.0 0.7 B18-4 1.6 0.3 B5-1 1.4 1.2 B6-2 1.5 1.2 B18-5 0.9 0.2 B5-2 1.8 0.9 B8 1.4 1.7 B7-1 1.7 1.4 B13-2 1.9 0.3 B7-2 1.5 0.9 B16-1 1.0 0.7 B17-1 1.9 2.0 B17-3 1.0 1.0 B20-2 0.9 0.5 Open-plan Office (Figures 3.12 and 3.18) Open-plan Office (Figures 3.13 and 3.19) Standard Room (Figures 3.14 and 3.20) Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m B1-3 1.6 0.2 B10-3 1.2 0.5 B4-3 0.6 0.6 B6-1 1.5 N/A B10-4 0.7 0.7 B20-1 0.2 0.2 B10-1 1.5 N/A B18-1 1.1 0.3 B21-1 0.1 0.1 B11-1 0.7 0.7 B18-3 1.1 0.3 B21-2 0.4 0.3 B11-2 2.5 1.5 B22-3-1 1.3 0.9 B22-1 0.6 N/A B12-1 0.8 0.8 B22-3-2 1.1 0.9 B22-2-1 0.4 N/A B12-2 1.4 1.7 B22-3-3 1.7 1.4 B22-2-2 0.9 0.1 B13-1 1.2 0.7 B22-4-1 0.2 0.4 B14-1 2.5 1.8 B22-4-2 0.3 0.2 B14-2 2.3 1.8 B22-4-3 1.2 0.1 B15-1 1.2 0.5 B22-4-4 0.1 N/A B15-2 0.8 0.5 B22-5-1 0.2 0.2 B16-2 1.6 1.5 B22-5-2 0.1 N/A B17-2 1.6 1.0 B22-6-1 0.6 0.6 B17-4 1.6 1.5 B22-6-2 0.4 0.3 B19 1.7 1.5 51 Table 3.7 - Maximum Regression Error Comparison Between Lp,S,A,1-16m and Lp,S,A,4m in dB. Open-plan Office (Figures 3.9 and 3.15) Open-plan Office (Figures 3.10 and 3.16) Open-plan Office (Figures 3.11 and 3.17) Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m B1-1 2.6 2.5 B9 1.4 0.4 B1-2 1.8 2.8 B2 1.9 0.8 B10-2 3.5 3.1 B4-1 3.3 1.5 B3-1 1.1 0.4 B18-2 1.5 0.4 B4-2 2.7 N/A B3-2 2.2 1.3 B18-4 3.8 0.5 B5-1 2.9 2.0 B6-2 2.6 2.1 B18-5 2.2 0.3 B5-2 3.2 1.5 B8 2.3 2.3 B7-1 3.4 2.6 B13-2 4.3 0.5 B7-2 2.6 1.6 B16-1 1.9 1.4 B17-1 4.5 4.0 B17-3 2.2 1.3 B20-2 2.2 1.4 Open-plan Office (Figures 3.12 and 3.18) Open-plan Office (Figures 3.13 and 3.19) Standard Room (Figures 3.14 and 3.20) Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m Room Ee-r,1-16m Ee-r,4m B1-3 2.7 0.4 B10-3 2.5 0.8 B4-3 0.8 0.8 B6-1 3.0 N/A B10-4 1.7 1.4 B20-1 0.5 0.4 B10-1 2.5 N/A B18-1 2.6 0.8 B21-1 0.2 0.1 B11-1 1.7 1.4 B18-3 2.6 0.8 B21-2 0.6 0.5 B11-2 4.3 2.3 B22-3-1 2.7 2.1 B22-1 0.7 N/A B12-1 2.4 2.5 B22-3-2 2.0 1.9 B22-2-1 0.6 N/A B12-2 4.5 3.8 B22-3-3 3.8 2.7 B22-2-2 1.2 0.1 B13-1 3.0 1.6 B22-4-1 0.7 0.6 B14-1 5.6 4.0 B22-4-2 0.9 0.2 B14-2 4.4 3.2 B22-4-3 2.1 0.2 B15-1 1.9 0.7 B22-4-4 0.2 N/A B15-2 1.5 0.6 B22-5-1 0.4 0.4 B16-2 2.7 3.1 B22-5-2 0.1 N/A B17-2 3.9 2.3 B22-6-1 0.9 0.8 B17-4 2.8 2.9 B22-6-2 0.6 0.5 B19 4.2 2.4 52 3.1.4.2 Discussion In open-plan offices, 𝐿𝑝,𝑠,𝐴 tended to show a consistent pattern in variability. 𝐿𝑝,𝑠,𝐴 tended to decrease sharply upon crossing a divider, but increase again before the next divider. This trend develops at decreasing distances with increasing divider height. This behavior is caused by a combination of ceiling reflections and dividers and is largely a function of geometry. While the direct sound is obstructed by the dividers, sound reflected from the ceiling enters pods of workspaces from above. Workspaces immediately behind dividers benefit from physical shielding. Workspaces located farther from the divider are no longer shielded from ceiling reflections, resulting in the potential for higher sound pressure levels despite being located farther from a noise source. Additionally, sound may diffract over the top edge of the workspace dividers. In outdoor noise propagation applications, diffraction is a significant consideration as the nearest receivers may be far away, and even small angles of diffraction will render the barrier ineffective. Therefore, the performance of outdoor noise barriers is dictated mainly by the height of the barrier. However, in indoor situations, the contribution of sound diffracting over the edges of workspace dividers may be insignificant compared to the sound reflected off the ceiling. In rooms where the ceiling is highly absorbent, diffraction may be a more significant contributor. A change in slope was also observed in some open-plan offices (henceforth referred to as double slopes). In general, double slopes were more common in open-plan offices with higher dividers. This is also likely to be due to ceiling reflections and geometry. Contributions from ceiling reflections result in a lower value of 𝐷𝐿2 at closer distances. Ceiling reflection contributions then decrease with increasing distance. In combination with high divider heights that provide more shielding, 𝐷𝐿2 at farther distances is expected to be higher than at closer distances. For open-plan offices, 𝐷𝐿2,𝑠,𝐴,1−16𝑚 ranged from 3.9 – 9.7 dB/DD, while 𝐷𝐿2,𝑆,𝐴,4𝑚 ranged from 3.9 – 13.8 dB/DD. Keranen observed similar values for 𝐷𝐿2,𝑆,𝐴,4𝑚, ranging from 4.0 – 12.4 dB/DD. 𝐷𝐿2,𝑆,𝐴,4𝑚 being typically higher in magnitude than 𝐷𝐿2,𝑠,𝐴,1−16𝑚 indicates that a double-slope is present. Additionally, the change in DL2 in open-plan offices is indicated by a visible increase in 53 estimation error present between 4 and 8 m in Figures 3.9 through 3.13, which also suggests that the double-slope is a non-trivial contribution to regression error for 𝐷𝐿2,𝑠,𝐴,1−16𝑚. A visible trend is present in the regression error for 𝐷𝐿2,𝑠,𝐴,1−16𝑚 (Figures 3.9 through 3.13). The regression error is typically positive at distances of between 4 – 8 m, and negative between distances of 1 – 4m and 8 m and beyond. For 𝐷𝐿2,𝑆,𝐴,4𝑚 (Figures 3.15 through 3.19), this trend is absent. This is consistent with Keranen specifying for measurements to start from 4 m to avoid systemic bias due to double-slopes. The range of estimation error for 𝐷𝐿2,𝑠,𝐴,1−16𝑚 was approximately 4 – -4 dB, while 𝐷𝐿2,𝑆,𝐴,4𝑚 was approximately -3 – 3 dB. The estimation error for 𝐷𝐿2,𝑠,𝐴,1−16𝑚 is expected to be a sum of both slope-change error and the sharp increases and decreases in 𝐿𝑝 before and after workspace dividers, whereas estimation error for 𝐷𝐿2,𝑆,𝐴,4𝑚 is expected to be entirely due to workspace dividers. Since workspace dividers were observed to cause overestimation of 𝐿𝑝𝑠,𝐴 behind diviers and underestimation before dividers, it should be possible to more accurately predict 𝐿𝑝𝑠,𝐴. 𝐷𝐿2,𝑠,𝐴,1−16𝑚 data can be used to study the onset of this behavior and its dependence on divider height, while 𝐷𝐿2,𝑠,𝐴,4𝑚 data may be used to further understand the magnitude of the overestimation and underestimation. 𝐷𝐿2,𝑠,𝐴,1−16𝑚 was 1.0 – 4.7 dB/DD for standard rooms. In the absence of obstructions, the direct sound transmission path 𝐷𝐿2 cannot exceed 6 dB/DD. The data measured in standard rooms matches this expectation. Prediction errors were also within 1.5 dB for all measured scenarios. Additionally, 𝐷𝐿2 was visually linear, suggesting that standard rooms may be sufficiently described using a single propagation curve. The Macmillan building on UBC’s Vancouver campus (building 22) was used for propagation direction and furnishing measurements. Room 4 was an acoustically untreated computer lab of approximately equal length and width where four DL2 measurements were conducted. In this room, 𝐷𝐿2 ranged from 1.7 – 3.0 dB/DD. The same behavior was observed in room 5, an acoustically treated computer lab that was similar to room 4. 𝐷𝐿2 values ranged from 2.7 – 4.7 54 dB/DD, suggesting that 𝐷𝐿2 is dependent on propagation direction, even in standard rooms. This behavior was likely caused by the geometry and room surfaces, like Hodgson’s observation that roof pitch in industrial rooms affected 𝐷𝐿2. 𝐷𝐿2 in the lunchroom (room 6) decreased from 2.5 dB/DD – 2.3 dB/DD when tables were introduced. Furnishing typically increases 𝐷𝐿2 in rooms but furnishing the lunchroom with tables appeared to decrease 𝐷𝐿2. This is speculated to be due to the orientation of the table as the tables were all parallel to the ground. The tabletops are acoustically reflective and effectively become a large acoustic reflector as opposed to volume scattering. Finally, it was noticed that measurement distances were not regularly spaced when placed on a logarithmic scale. In B22, it was noted that measurements were occurring at higher densities at larger distances. This may be a source or regression error as the 𝐷𝐿2 value is biased towards the distant data points. This could be resolved by collecting measurement data at locations which increase in distance by a constant factor (e.g. 2 times, 21/2 times, 21/3 times etc.). The regular intervals will give each measurement equal weighting in their contributions to the 𝐷𝐿2 value. 3.1.4.3 Conclusion 𝐷𝐿2 was measured in 62 rooms in 22 buildings. 𝐷𝐿2 was calculated using data from distances between 1 – 16 m (𝐷𝐿2,𝑠,𝐴,1−16𝑚), and between 4 m and the maximum allowable distance in the rooms (𝐷𝐿2,𝑠,𝐴,4𝑚) with the objective of assessing the linear decay of 𝐿𝑝,𝑠,𝐴 on a logarithmic distance scale. Double slopes were observed in open-plan offices at around 4 – 8 m from the source, revealing 1 – 2 dB of underestimation for (𝐷𝐿2,𝑠,𝐴,1−16𝑚 regressions. As 𝐷𝐿2,𝑠,𝐴,4𝑚 was chosen to avoid changes in slope, no estimation errors were observed. The prediction accuracy of both 𝐷𝐿2,𝑠,𝐴,1−16𝑚 and 𝐷𝐿2,𝑠,𝐴,4𝑚 suffered due to the tendency for 𝐿𝑝,𝑠,𝐴 to increase before, and decrease significantly after dividers. The onset of this behavior is hypothesized to be a function of divider height. Estimation error in 𝐷𝐿2,𝑠,𝐴,1−16𝑚 is expected to be a combination of both slope-change and divider-related errors. By visual inspection, double-slope errors appeared to account for 1 – 2 dB of deviation. 𝐷𝐿2,𝑠,𝐴,4𝑚 error data was used to determine that the overestimation and 55 underestimation due to the presence of dividers accounted for approximately 3 dB of deviation. Further experimentation is recommended at finer measurement resolution to better study how workspace divider arrangements cause deviations from 𝐷𝐿2 regressions. 𝐷𝐿2 in standard rooms was linear over the entire range; estimation errors were typically within 1 dB. Two computer labs were measured: one treated, and one untreated. 𝐷𝐿2 was 1.7 – 3.0 dB/DD in the untreated case and 2.7 – 4.7 dB/DD in the other. Measurements along different propagation directions in the same room resulted in different 𝐷𝐿2 values, suggesting that 𝐷𝐿2 is dependent on direction. This behavior is hypothesized to be caused by the distribution of acoustic absorption and the distribution of volume scattering. In the model, standard rooms will not require any adjustments. Open plan offices will be adjusted by 1 – 2 dB in the range of 4 – 8 m from a sound source. Further investigation is required to understand the impact of workspace dividers. From a measurement perspective, 𝐷𝐿2 may be more widely adopted if the measurement distances were applicable regardless of room type. While measurements from 1 – 16 m are associated with 𝐷𝐿2 regression errors in open plan offices, the errors are predictable. This is an acceptable trade-off for a universal DL2 measurement method. The measurement distances are recommended to be taken at distances that are multiples of the previous distance (e.g. 1, 2, 4, 8, 16 m) as opposed to fixed measurement increments (e.g. 1, 2, 3, 4, 5, 6 m) to avoid regression bias in the 𝐷𝐿2 value. 3.1.5 𝐿𝑝,1𝑚 3.1.5.1 Measurement Results Sound pressure level at 1 m from DL2 measurements and speech intelligibility measurements (conducted at the same time as the DL2 measurements) were compiled. The data was sorted by octave band then categorized under open-plan office or standard rooms. To examine the deviation from expected free-field decay levels, the sound pressure level of a point source in a free-field environment at 1 m (𝐿𝑝,1𝑚,𝐹𝐹) as predicted by Eq. (1.5) was subtracted from each 𝐿𝑝,1𝑚 measurement. The results are shown as a function of room volume in Figures 3.21 56 through 3.27. Three regressions were applied to each frequency band: (1) a logarithmic regression for standard rooms in regular font; (2) a linear regression for the open plan offices in italicized font; and (3), a logarithmic regression for the entire dataset in bold-faced font. For standard rooms, the difference between 𝐿𝑝,1𝑚 and 𝐿𝑝,1𝑚,𝐹𝐹 decreased with increasing volume in all bands. The correlation coefficient was lowest in the 125 Hz band (r2 = 0.016) and was significantly higher in other bands (r2 = 0.082 – 0.179). For open-plan offices, linear regressions yielded the highest r-squared value. In the 125 – 1,000 Hz bands, the regression predicted similar values for 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 over the range of 30 – 1,000 m3; the slope of these four bands ranges from -4x10-4 – -1.2x10-3 dB/m3. In the 2,000 – 8,000 bands, the regression slope ranged from -2.9x10-3 – -0.45x10-3 dB/m3. In all cases, the highest r-squared values, ranging from 0.10 – 0.27, were achieved by applying a logarithmic regression to the entire data set. In the 125, 2,000, 4,000 and 8,000 Hz bands, many data points were negative, suggesting that 𝐿𝑝,1𝑚 is lower in rooms than in a free-field environment. The 125 Hz band contained the most negative values. The 2,000 – 8,000 Hz bands had identical numbers of negative values. Additionally, the negative values all appear to be from the same measurements as they occur at the same volumes. 57 Figure 3.21 - 𝑳𝒑,𝟏𝒎 - 𝑳𝒑,𝟏𝒎,𝑭𝑭 for 125 Hz Band. Figure 3.22 - 𝑳𝒑,𝟏𝒎 - 𝑳𝒑,𝟏𝒎,𝑭𝑭 for 250 Hz Band. 58 Figure 3.23 - 𝑳𝒑,𝟏𝒎 - 𝑳𝒑,𝟏𝒎,𝑭𝑭 for 500 Hz Band. Figure 3.24 - 𝑳𝒑,𝟏𝒎 - 𝑳𝒑,𝟏𝒎,𝑭𝑭 for 1,000 Hz Band. 59 Figure 3.25 - 𝑳𝒑,𝟏𝒎 - 𝑳𝒑,𝟏𝒎,𝑭𝑭 for 2,000 Hz Band. Figure 3.26 - 𝑳𝒑,𝟏𝒎 - 𝑳𝒑,𝟏𝒎,𝑭𝑭 for 4,000 Hz Band. 60 Figure 3.27 - 𝑳𝒑,𝟏𝒎 - 𝑳𝒑,𝟏𝒎,𝑭𝑭 for 8,000 Hz Band. 3.1.5.2 Discussion Low r2 values were expected for all frequency bands as the regression assumed that room volume was the only factor influencing 𝐿𝑝,1𝑚. Additionally, all rooms were assumed to be ‘normally furnished’ (e.g. suspended acoustic ceilings, carpeting), where the surfaces in the room are neither highly absorptive nor reflective. However, the r2 value for the 125 Hz band was particularly low. This was likely due to some measurements being taken where the source and receiver were located across a table. This configuration was common as some of the 𝐿𝑝,1𝑚 data was taken from speech intelligibility studies, which simulated scenarios such as meetings in private offices across a desk. As the source and receiver were both at heights of 1.2 m, tables or desks of 0.75 m height would then be within 0.45 m of the source-receiver pair. As the quarter-wavelength of the 125 Hz band is 0.69 m, this large data scatter could be due to a combination of the Waterhouse Effect (where the source is very close to the edge of the table) and interference effects (which depends on the length of the first-order reflection path caused by the height of the table). Additionally, at a wavelength of 2.7 m, in 61 the 125 Hz band, there could have been standing wave effects, as many rooms were around 2.7 m in height. In the 2,000 – 8,000 Hz bands, there were many negative values for 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹, with the most in the 8,000 Hz band. The data points appeared to be from the same data measurements, as the room volumes were identical. Additionally, the trends in the negative values in these bands were similar. This is likely due to the directivity of the dodecahedral array, since this behavior is less apparent in the other frequency bands. As the calibration of the array was a randomized sample of 40 measurements, little was known about the directivity pattern at higher frequency bands. The directivity pattern of the array should be studied in greater detail to understand how closely dodecahedral loudspeaker arrays emulate omni-directional point sources. Linear regressions yielded the highest r2 values for open plan office datasets. As slopes ranged from -4.0x10-4 – -2.9x10-3 dB/m3, 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 appeared to be independent of room volume. This is likely due to how open plan offices are typically furnished – all workspaces in open plan offices will have a desktop and dividers nearby regardless of the size of the office itself. Additionally, the typically large size of open plan offices resulted in the nearest surfaces being the desk and dividers. Therefore, 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 depends mostly on the local acoustical environment: subsections of the office space created by workspace dividers. In all octave bands, logarithmic regressions yielded the highest r2 values when applied to the entire dataset. In logarithmic regressions, the coefficient for the logarithmic term is the rate of change per magnitude. For base-10 regressions, the coefficient for the logarithmic term is the amount of change per multiplication of 10. In the context of room volumes, the greatest changes in 𝐿𝑝,1𝑚 occurred at lower room volumes, and smallest changes occurred at higher room volumes. A logarithmic regression takes into consideration both the rapid decrease in 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 for standard rooms, and the nearly volume-independent behavior in open plan offices. Finally, it should be acknowledged that dodecahedral loudspeaker arrays have a finite size. The measurements were taken 1 m from the centre of the loudspeaker array. This effectively means that the measurements were taken at a distance that is the radius of the array less than 1 m. This is expected to cause the measured level to be higher than what Eq. (1.5) predicts. 62 3.1.5.3 Conclusion Experimental 𝐿𝑝,1𝑚 values differ from what the expected free-field decay is for an omni-directional point source. The relationship between 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 appeared to be logarithmically dependent on room volume. For normally furnished rooms (i.e., with all surfaces neither highly absorptive nor highly reflective), a logarithmic 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 prediction model was introduced for each octave band, which was implemented in the finalized 𝐷𝐿2 model. 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 appeared to stabilize at larger volumes in all frequency bands. The behavior was attributed to the use of workspace screens in open plan offices. Negative values for 𝐿𝑝,1𝑚 – 𝐿𝑝,1𝑚,𝐹𝐹 were observed in all bands, and were most common in the 125, 4,000 and 8,000 Hz bands. The 125 Hz band discrepancy was likely to be destructive interference due to surfaces being located around 0.7 m from the source, while the 4,000 and 8,000 Hz bands were likely due to the directivity pattern of the dodecahedral loudspeaker array used as the source in the measurements. 63 4 Complete 𝐷𝐿2 vs 𝑆𝑇𝐼 Model In this chapter, the model for predicting room acoustic quality as a function of 𝐷𝐿2 introduced in Chapter 2 will be modified to include the experimental observations in Chapter 3.1. Additionally, the 𝑆𝑇𝐼 calculation scheme (Eq.(2.1) through (2.3)) will be substituted with a form that accounts for the contributions of direct speech to intelligibility. Finalized 𝑆𝑇𝐼 calculation tools, implemented as Microsoft Excel spreadsheets, are available for download from the cIRcle collection of Supplementary Thesis Materials and Errata. 4.1 Model Components 4.1.1 Modulation Transfer Function (Direct Speech) As of Chapter 2, the 𝐷𝐿2 vs 𝑆𝑇𝐼 model used only the reveberant-speech modulation transfer function and was therefore limited to rooms where the direct speech is absent. This limited the model to rooms such as open plan offices, where there is usually no direct line of sight between a talker and listeners other than the intended recipient of speech. By including the contributions of direct speech in the modulation transfer function, all rooms may be assessed. In addition to formulating the modulation transfer function for calculating the speech transmission index using only indirect sound, Houtgast and Steeneken derived a formulation which includes direct speech [1]. The modulation transfer function including direct speech is as follows: 𝑚(𝑓) =(𝐴2 + 𝐵2)0.5𝐶 (4.1) With: 𝐴 =𝑄𝑡𝑄𝑟2+1𝑟𝑐2 [1 + (2𝜋𝑇𝑓 13.8)2]−1 (4.2) 𝐵 =1𝑟𝑐22𝜋𝑇𝑓 13.8 [1 + (2𝜋𝑇𝑓 13.8)2]−1 (4.3) 64 𝐶 =𝑄𝑡𝑄𝑙𝑟2+1𝑟𝑐2 + 𝑄𝑡10(𝐿𝑛−𝐿𝐴,𝑠,1𝑚)/10 (4.4) Where: 𝑚(𝑓) is the modulation transfer function at frequency 𝑓 𝑓 is the modulation frequency (from 0.4 – 30 Hz at third octave intervals) 𝑄𝑡 is the directivity index of a human talker (see Table 2.3) 𝑄𝑙 is the directivity index of the listener (stated to be 1.5 by the author [1]) 𝑟 is the distance between the talker and the listener 𝑟𝑐 is the critical radius of the room 𝑇 is the reverberation time in seconds (assumed to be 𝑇20) 𝐿𝑛 is the background noise sound pressure level at the listener’s location 𝐿𝐴,𝑠,1𝑚 is the free-field speech pressure level of the talker at 1 m in front of the talker’s mouth However, this formulation of the modulation transfer function was intended to be used at the design level [1] and therefore does not use quantities that are measured when evaluating 𝐷𝐿2. In 𝐷𝐿2 evaluations, the only measured quantities are the reverberation time, background noise level, distance, and total measured sound pressure. The volume of the room is sometimes measured as well. To circumvent this limitation, the assumptions employed in the development of Houtgast and Steeneken’s formation were examined. In the derivation of the direct sound modulation transfer function, a squared impulse response (or echogram) for the room was assumed and is defined as follows: 𝑟(𝑡) = 𝑟𝑑(𝑡) + 𝑟𝑟(𝑡) (4.5) Where: 𝑟(𝑡) is the total squared impulse response for the room 𝑟𝑑(𝑡) is the direct sound contribution to the impulse response 𝑟𝑖(𝑡) is the indirect sound contribution to the impulse response 65 The direct sound contribution to the impulse response is then defined as: 𝑟𝑑(𝑡) = (𝑡𝑟2) 𝛿(𝑡) (4.6) Where: 𝑡 is time 𝑟 is distance 𝛿 is the dirac-pulse function and the indirect sound contribution is defined as: 𝑟𝑖 =1𝑟𝑐213.8𝑇𝑒−13.8𝑡/𝑇 (4.7) Where: 𝑇 is the reverberation time 𝑟𝑐 is the critical radius Eq. (4.6) states that the direct sound is only a function of distance, and is identical to Eq. (1.5). Eq. (4.7) uses diffuse field theory to define the indirect sound. The direct and indirect sound contributions to the room impulse response appear in the modulation transfer function (Eq. (4.1) through (4.4)) as the distance between the talker and the listener (𝑟) and the critical distance (𝑟𝑐) of the room respectively. The total speech pressure level is then calculated as a function of distance and the critical distance. As the direct sound modulation transfer function (Eq. (4.1)) was originally intended for design stage calculations, the use of diffuse field theory was expected. However as previously discussed, diffuse field theory rarely holds true for real rooms and the indirect speech pressure level also depends on distance, hence the proposition of 𝐷𝐿2 as a universal parameter. To calculate the speech transmission index using Eq. (4.1) such that the reverberant speech pressure level may be defined, the critical radius must be defined such that it results in the measured reverberant speech pressure level. 66 The critical radius is defined as the distance where the direct speech pressure level is equivalent to the reverberant speech pressure level: 𝐿𝑝,𝑑𝑖𝑟𝑒𝑐𝑡 = 𝐿𝑝,𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡 (4.8) The direct speech component is then defined using Eq. (1.4). By evaluating the direct speech at the critical radius, the following relationship holds true: 𝐿𝑝,𝑑𝑖𝑟𝑒𝑐𝑡 = 𝐿𝑤 + 10𝑙𝑜𝑔 [𝑄𝛳4𝜋𝑟𝑐2] = 𝐿𝑝,𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡 (4.9) Eq. (4.9) may then be rearranged to yield the critical radius as a function of known parameters: 𝑟𝑐 = (𝑄𝜃 4𝜋10(𝐿𝑝,𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡−𝐿𝑤)/10 )0.5 (4.10) The critical radius yielded by Eq. (4.10) allows the use of a user-defined reverberant speech pressure level in Eq. (4.1). By defining the distance, r, to be infinitely large, Eq. (4.1) is expected to yield the same result as Eq. (2.1) for the same reverberant speech pressure level, reverberation time, and background noise level. This was verified by calculating the speech transmission index using a defined reverberant speech pressure level in Eq. (2.1) and comparing the results to a critical radius calculated using Eq. (4.10) in Eq. (4.1) for an infinitely large talker-listener distance. It was noted that the background noise level term in Eq. (4.4) is modified by the talker’s directivity. This was theorized to be incorrect as increasing the talker directivity is expected to increase speech intelligibility. However, if Eq. (4.4) is applied with the talker’s directivity modifying the background noise level term, the calculated intelligibility decreases as the talker’s directivity increases. It was then proposed that the talker directivity term be removed from the background noise level term of Eq. (4.4), resulting in the following: 𝐶 =𝑞𝑡𝑞𝑙𝑟2+1𝑟𝑐2 + 10(𝐿𝑛−𝐿𝑠𝑝1𝑚)/10 (4.11) 67 By redefining the critical radius in terms of the reverberant speech pressure level, Eq. (4.1) may be used with parameters available from 𝐷𝐿2. In the case where the total sound pressure level is less than the expected direct speech sound pressure level, the total sound pressure level is assumed to be entirely indirect. 4.1.2 Experiment-Based Modifications to 𝐷𝐿2 Model This chapter reiterates the findings from Chapter 3.1 as improvements to the 𝐷𝐿2 model. The original assumptions were made under the pretense that they would be adjusted using observations from data in real rooms. The assumptions employed in Chapter 2.1 that are applicable specifically to 𝐷𝐿2 are listed in Table 4.1. Table 4.1 - Assumptions Employed in the Idealized DL2 Model and their Conditions Assumption Condition Sound Pressure Level at 1 m (𝑳𝒑,𝟏𝒎) The sound pressure level at a distance of 1 m from a sound source is assumed to be equal to that of what it is expected to be in a free field. Uniform, Broadband Decay The value for DL2 is identical for all octave bands. Therefore, the A-weighted speech pressure level can be used as a representative term. Linear Decay The decrement of sound is expected to be linear. That is, a single value of 𝐷𝐿2 is sufficient to describe the decrement of sound at all distances form a sound source in a room. 4.1.2.1 Sound Pressure Level at 1 m (𝐿𝑝,1𝑚) This assumption was assessed in Chapter 3.1.5. Sound pressure level data at 1 m from a dodecahedral loudspeaker array was collected in 53 rooms. As expected, it was found that the sound pressure level in rooms is rarely equal to the level expected in a free field environment. In the absence of other room furnishing information, it was assumed that all the rooms are normally furnished, and that room volume is the only factor determining the deviation from free-field behavior. 68 The data was sorted into octave bands and regressions were applied. Logarithmic regressions for the sound pressure level data at 1 m from the measurement loudspeaker produced the best r2-value. The regressions are shown in Table 4.2. Table 4.2 - Regression Equations Relating Sound Pressure Level at 1 m and Room Volume Frequency [Hz] Regression [dB] Correlation Coefficient 125 𝐿𝑝,1𝑚 = −0.855𝑙𝑛(𝑉) + 7.2680 0.1033 250 𝐿𝑝,1𝑚 = −1.059𝑙𝑛(𝑉) + 9.5802 0.2442 500 𝐿𝑝,1𝑚 = −0.784𝑙𝑛(𝑉) + 7.2882 0.2156 1,000 𝐿𝑝,1𝑚 = −1.014𝑙𝑛(𝑉) + 9.3390 0.2737 2,000 𝐿𝑝,1𝑚 = −1.034𝑙𝑛(𝑉) + 9.0132 0.2027 4,000 𝐿𝑝,1𝑚 = −1.148𝑙𝑛(𝑉) + 9.8664 0.1626 8,000 𝐿𝑝,1𝑚 = −1.348𝑙𝑛(𝑉) + 8.7639 0.1521 The regressions were then used to calculate the total sound pressure level at 1 m. This is the sound pressure level the 𝐷𝐿2 value is then applied to when calculating the sound pressure level at farther distances. 4.1.2.2 Uniform, Broadband Decay The 𝐷𝐿2 data collected in all of the rooms were compiled and an A-weighted speech pressure level 𝐷𝐿2 value was calculated for each data set. For each data set, the difference between the octave band 𝐷𝐿2 value and the A-weighted 𝐷𝐿2 was evaluated. The average and standard deviations of the averages are compiled in both open plan offices and standard rooms in Table 4.3. 69 Table 4.3 - Average Difference for DL2,f - DL2,s,A for (1) Open-plan Offices and (2) Standard Rooms in dB/DD. Open-plan Offices Frequency [Hz] 125 250 500 1000 2000 4000 8000 Average [dB/DD] -2.5 -0.7 0.1 0.9 0.7 0.4 0.7 St. Dev [dB/DD] 1.4 0.7 0.3 0.6 0.8 0.9 1.0 Standard Rooms Frequency [Hz] 125 250 500 1000 2000 4000 8000 Average [dB/DD] -0.1 -0.1 0.1 0.0 -0.1 0.2 0.9 St. Dev [dB/DD] 0.9 0.5 0.2 0.2 0.3 0.5 0.8 The 𝐷𝐿2 model was modified such that the user-input quantity is the 𝐷𝐿2 for the A-weighted speech pressure level. The 𝐷𝐿2 values for each octave band are then adjusted in accordance to Table 4.3. Since the spectral behavior of 𝐷𝐿2 was observed to vary between open plan offices and standard rooms, the room type will also determine which set of adjustments are to be applied. 4.1.2.3 Linear Decay In standard rooms, the regression error between 𝐷𝐿2 from 1 – 16 meters and the measured sound pressure level was generally within 1 dB. This was considered acceptable by the author in terms of regression accuracy. As such, a single value of 𝐷𝐿2 was deemed to be acceptable for applications where there is a direct line of sight between a talker and a listener. In open plan offices, the regression error depended largely on the presence of office dividers. The dividers were observed to systematically cause DL2 regression underestimations in front of a workspace divider and overestimations behind a workspace divider. In the distance range of 4 – 8 m, the regression error was approximately 2 dB. This was accounted for by adding a 1 dB adjustment to the sound pressure levels at 4 and 8 m, and a 2 dB adjustment to the sound pressure levels at 5 – 7 m. 70 4.2 Model Construction The model, as described in chapter 2.1.3, was then modified using the modified STI calculation scheme (direct sound), and according to experimental observations from chapter 3. A screenshot of the updated spreadsheet is shown in Figure 4.1. Figure 4.1 - Screenshot of Data Entry sheet of finalized DL2 calculation tool From the previous version, the common data sheet was merged with the data entry sheet. The NCB spectra for background noise were added and were referenced using a dropdown menu. Other than field labels, cells in blue require user input. That is, the user specifies the speech vocal effort level, the background noise level, the reverberation time, the broadband 𝐷𝐿2 value, the type of room, the room size, and the presence of a divider, if applicable. The spreadsheet uses the speech vocal effort spectrum to calculate the 1 m speech pressure level, and adjusts it using the room volume according to Table 4.2. The speech pressure levels are then calculated at distances increasing by factors of 1.4 times using the user-specified 𝐷𝐿2 value (modified by the broadband decay adjustments in Table 4.3). 71 For open plan offices, 1 dB is added to speech pressure levels occurring at distances between 4 – 5 m, and 7 – 8 m, and 2 dB are added to speech pressure levels occurring at distances between 5 – 7 m. The model is then formatted in two ways: an 𝑆𝑇𝐼 vs Distance format for examining how 𝑆𝑇𝐼 decays for a given set of conditions, and an 𝑆𝑇𝐼 vs 𝐷𝐿2 format for examining how STI varies with 𝐷𝐿2 at a fixed listener position. While it was noted that dividers will result in higher sound pressure levels before the divider and lower sound pressure levels after, the effects were not examined in enough detail to be included in the model. In general, one can expect a 1 – 3 dB increase before a divider, and about a 1 – 3 dB decrease after a divider. This is not yet considered and needs to be manually accounted for by the user. 4.2.1 𝑆𝑇𝐼 vs Distance In this format, the 𝐷𝐿2 for the A-weighted speech pressure level is specified. The total speech pressure level is then calculated for each octave band after applying the 𝐷𝐿2 adjustment values in Table 4.3 to the specified A-weighted speech pressure level 𝐷𝐿2 value. The total speech sound pressure levels are then calculated at 1, 1.4, 2, 2.8, 4, 5.7, 8, 11.3, and 16 meters. The direct speech sound pressure level is then calculated at the same distances using Eq. (1.5). The reverberant speech sound pressure level is calculated by decibel subtraction using Eq. (1.6). The calculated reverberant speech sound pressure levels are then used to calculate the equivalent critical radius, 𝑟𝑐, at each calculation position using Eq. (4.10). The input quantities are then applied to Eq. (4.1) to evaluate 𝑆𝑇𝐼. It was postulated that if the expected direct speech sound pressure level exceeds the total sound pressure level, the total sound is comprised entirely of indirect sound. At locations where this occurs, the distance term used in Eq. (4.1) is set to an infinitely large quantity such that Eq. (4.1) evaluates the reverberant speech 𝑆𝑇𝐼. 72 For open plan offices, a +1 dB adjustment is added to the sound pressure levels at 4 and 8 m, and a +2 dB adjustment is added to the sound pressure levels at 5 – 7 m to account for the presence of the double slope. The adjustments translate to an approximate increase in 𝑆𝑇𝐼 of 0.03 and 0.06. Figure 4.2 shows a sample 𝑆𝑇𝐼 vs Distance plot for a talker speaking at Normal vocal effort in an open plan office that is 2.7 m in height, 18 m in length, and 10 m in width. The reverberation time is 0.8 s, the background noise spectrum is NCB-30 and the 𝐷𝐿2 is 8 dB/DD. Figure 4.2 - Sample STI vs Distance plot for an Open Plan Office Figure 4.3 shows a sample 𝑆𝑇𝐼 vs Distance plot for a talker speaking at Normal vocal effort in a standard room that is 2.7 m in height, 8 m in length, and 6 m in width. The reverberation time is 0.4 s, the background noise spectrum is NCB-20 and the DL2 is 3 dB/DD. 73 Figure 4.3 - Sample STI vs Distance plot for a Standard Room 4.2.2 𝑆𝑇𝐼 vs 𝐷𝐿2 In this format, the evaluation distance is specified. The total speech pressure level at the specified distance is calculated for values of 𝐷𝐿2 between 1 – 14 dB/DD using the 𝐷𝐿2 adjustments in Table 4.3. If the distance is between 4 and 8 m in an open plan office setting, a +1 dB adjustment is applied to the total speech pressure level at 4 and 8 m, and a +2 dB adjustment is applied to the total speech pressure level at 5 – 6 m. The direct speech pressure level is then calculated at the specified distance. The indirect sound is calculated by decibel subtraction of the direct speech pressure level from the total speech pressure level and is then converted to a critical distance value, 𝑟𝑐, value. Eq. (4.1) is then used to evaluate the 𝑆𝑇𝐼. Figure 4.4 shows a sample 𝑆𝑇𝐼 vs 𝐷𝐿2 plot for the same standard room as in Figure 4.3, evaluated at the transition distance of 4 m from a talker. However, there is an unexpected increase in 𝑆𝑇𝐼 around 6 dB/DD. This increase was theorized to be a result of a commonly recognized error in decibel subtraction as illustrated by the following example where sound pressure level 1 (𝐿1) is to be subtracted from sound pressure level 2 (𝐿2). As 𝐿1 approaches 𝐿2, the resulting sound pressure level approaches zero. This artefact is widely acknowledged in acoustical engineering and standards include provisions for a lower-limit estimation of the resulting sound pressure level. Clause 11.8.2 74 in ASTM Standard E336-14 “Standard Test Method for Measurement of Airborne Sound Attenuation between Rooms in Buildings” states that If 𝐿1 is within 5 dB of 𝐿2, the resulting sound pressure is approximate as being 2 dB lower than 𝐿2 [19]. Figure 4.4 - Sample STI vs DL2 plot showing Artefact of Decibel Subtraction around 6 dB/DD Range Figure 4.5 results when approximating the reverberant speech pressure level as per E336 for situations where low signal to noise ratio is an issue. Contrary to the initial postulation that the increase in 𝑆𝑇𝐼 as 𝐷𝐿2 approaches 6 dB/DD, the increase in 𝑆𝑇𝐼 is still present. To diagnose the cause of the increase in 𝑆𝑇𝐼, a sensitivity check was conducted by varying the critical radius in Eq. (4.1). It was found that 𝑆𝑇𝐼 increased as the critical radius increased, meaning that the reverberant speech pressure level reduces the speech intelligibility of direct speech. 75 Figure 4.5 - Sample 𝑺𝑻𝑰 vs 𝑫𝑳𝟐 plot with E336-15 Adjustment for Decibel Subtraction Approximation for Low 𝑺/𝑵 As Figure 4.5 appeared to produce results that were similar to Figure 4.4 while accounting for the presence of reverberant speech pressure level, the E336-14 adjustments were made to the 𝑆𝑇𝐼 vs Distance model as well. 4.3 Sample Applications In this section, the completed model will be used to evaluate theoretical rooms with the rating criteria formulated in Chapter 2 (Tables 2.7 through 2.9). This exercise is intended to give readers insight to how the models may be used and for the authors to identify any errors or logical fallacies in the formulation of the model through sample applications. 4.3.1 Case 1 (Intelligibility) The 𝑆𝑇𝐼 vs 𝐷𝐿2 model was used to evaluate two theoretical classrooms: one which conforms to standards and one which does not. According to British Standard BB93 the maximum recommended background noise level is 35 dBA (approximately equal to NCB-25) and the maximum recommended reverberation time is 0.8 seconds for new classrooms [20]. The theoretical classroom was assumed to be 2.7 m in height, 10 m in width and 12 m in length. The talker was assumed to be speaking at a normal vocal effort. 76 The evaluation point, or transition distance, was chosen to be at the back of the classroom, at approximately 10 m from the talker. For quick reference, the quality ratings for Case 1 (intelligibility) rooms (Table 2.7) are provided below. Since an evaluation point is known, the 𝑆𝑇𝐼 vs 𝐷𝐿2 model was used. Effort Rating Listening Effort STI Range Intelligibility % Acceptable Rating 1 Very little effort 0.73 – 1.00 100 Yes Excellent 3 Little effort 0.62 – 0.73 100 Yes Good 5 Moderate effort 0.53 – 0.62 100 Yes Poor 7 Considerable effort 0.43 – 0.53 100 Yes Bad 9 Much effort 0.35 – 0.43 88% No N/A 11 Extreme effort 0.30 – 0.35 80% No N/A Figure 4.6 shows 𝑆𝑇𝐼 as a function of 𝐷𝐿2 at 10 m from the talker for a compliant classroom. In classrooms, 𝐷𝐿2 will never exceed 6 dB/DD as 6 dB/DD is interpreted as an anechoic environment. For a classroom that is compliant with the limits specified by BB93, all 𝐷𝐿2 values below 5 dB/DD require little listening effort. Figure 4.6 - 𝑺𝑻𝑰 vs 𝑫𝑳𝟐 at 10 m from a talker for a compliant classroom (𝑳𝒏 = 35 dBA, 𝑻 = 0.8 s) 77 Figure 4.7 shows 𝑆𝑇𝐼 as a function of 𝐷𝐿2 at 10m from the talker for a non-compliant classroom. The background noise level was chosen to be 40 dBA (NCB-30) and the reverberation time was chosen to be 1 second. At these conditions, the farthest listening position would require moderate or considerable listening effort. Figure 4.7 - 𝑺𝑻𝑰 vs 𝑫𝑳𝟐 at 10 m from a talker for a non-compliant classroom (𝑳𝒏 = 40 dBA, 𝑻 = 1.0 s) When a classroom is evaluated for acoustical quality, the background noise level and reverberation time are typically measured. Should it be that the classroom is found to be non-compliant, a 𝐷𝐿2 measurement would help room users decide the maximum allowable seating distance. Figure 4.8 shows 𝑆𝑇𝐼 vs Distance assuming a measured 𝐷𝐿2 of 3 dB/DD for the classroom in Figure 4.7. In this classroom, considerable listening effort is required at distances greater than 8 m. 78 Figure 4.8 - 𝑺𝑻𝑰 vs Distance for hypothetical non-compliant classroom in Figure 4.7 (𝑳𝒏 = 35 dBA, 𝑻 = 0.8 s) 4.3.2 Case 2 (Distraction) Case 2 was used to evaluate a theoretical study room. This room was also modeled to be compliant with BB93, with a background noise level of 40 dBA (NCB-30) and a reverberation time of 0.8 s. The distraction percentages in Table 2.8 are provided below for reference. Rating Loss of Productivity [%] 𝑺𝑻𝑰 Excellent 0 0.00 – 0.20 Good 0 – 2 0.20 – 0.35 Fair 2 – 4 0.35 – 0.43 Poor 4 – 6 0.43 – 0.50 Bad 6 – 7 0.50 – 0.60 Unacceptable > 7 > 0.60 The room was arbitrarily assumed to be 2.7 m in height, 25 m in length and 15 m in width and was assumed to contain dividers, such that the direct sound is not present. In this assessment, we were interested in the required 𝐷𝐿2 to reduce speech distraction at a nearby listening position. As 79 this room was modeled to be a study environment, talkers were expected to be speaking at a lowered (casual) speech effort level. Initially, the 𝑆𝑇𝐼 vs 𝐷𝐿2 was assessed at various distances to assess the possibility of reduced distraction. Since dividers are in place, the total sound reaching a distracted listener was assumed to contain no direct speech. Since the listener location is known, the 𝑆𝑇𝐼 vs 𝐷𝐿2 model was used. Figure 4.9 shows the 𝑆𝑇𝐼 vs 𝐷𝐿2 for listener locations at 4, 6, 8 and 10 m from the talker. This theoretical study room may be considered as being similar to an open plan office due to the presence of desk dividers. According to Table 3.5, the observed value for 𝐷𝐿2 ranges from 4 – 9 dB/DD. At a 𝐷𝐿2 of 4 dB/DD, a listener located at 4 m can expect to suffer about 2 – 4% of productivity loss. By knowing realistic 𝐷𝐿2 values and how to achieve them, this model can help designers determine the amount of furnishing and furnishing configuration to best reduce speech distraction. Figure 4.9 - 𝑺𝑻𝑰 vs 𝑫𝑳𝟐 at distances of 4, 6, 8 and 10 m for a hypothetical study room (𝑳𝒏 = 30 dBA, 𝑻 = 0.8 s) 4.3.3 Case 3 (Privacy) Case 3 was used to evaluate a theoretical eating establishment for privacy from other patrons. The privacy rating values from Table 2.9 are supplied below. 80 Rating Intelligible Speech [%] STI Excellent < 50 < 0.15 Good 50 – 60 0.15 – 0.20 Fair 60 – 80 0.20 – 0.27 Poor 80 – 90 0.27 – 0.35 Bad 90 – 100 0.36 – 0.43 Unacceptable > 100 > 0.43 The eating establishment was assumed to be similar to Dining Rooms according to BB93, which has a recommended background noise level of 45 dBA (approximately NCB-35) and reverberation time of 1 s. The eating establishment was arbitrarily assumed to be 2.7 m in height, and 15 m in width and length. Patrons in this setting were theorized to speak at normal vocal effort. Intended listeners were assumed to be located 1 m away, while the nearest unintended listener was assumed to be located 4 m away. Since a listener position was known, the 𝑆𝑇𝐼 vs 𝐷𝐿2 model was used to evaluate the 𝐷𝐿2 required to provide good speech privacy. Figure 4.10 shows the expected 𝑆𝑇𝐼 vs 𝐷𝐿2 for an unwanted listener located 4 m from a talker. Figure 4.10 - 𝑺𝑻𝑰 vs 𝑫𝑳𝟐 at 4 m for a hypothetical eating establishment without booths (𝑳𝒏 = 40 dBA, 𝑻 = 1 s) 81 Without booths, restaurants are best modeled as standard rooms, which are generally expected to have 𝐷𝐿2 values between 1 – 5 dB/DD. For standard eating establishment conditions, an unintended listener is expected to be able to hear the entire contents of a conversation at normal vocal effort. Some eating establishments, such as pubs, overcome lack of speech privacy by playing loud music. However, this in turn causes patrons to raise their voices in order to be heard, and the eating establishment may become uncomfortably loud. Figure 4.11 shows the same eating establishment with booths, with an unwanted listener located 4 m away, at different background noise levels. With booths in place, and by raising the background level to NCB-40 (50 dBA), good speech privacy (𝑆𝑇𝐼 < 0.20) can be achieved with 𝐷𝐿2 values of around 6 dB/DD. Figure 4.11 - 𝑺𝑻𝑰 vs 𝑫𝑳𝟐 at 4 m for eating establishment with booths at varying noise levels (𝑳𝒏 = 40 dBA, 𝑻 = 1 s) 4.4 𝐷𝐿2 Observations 4.4.1 Case 1 (Intelligibility) It was found that for a classroom of typical size, compliance with recommended reverberation time and background noise levels resulted in fully audible sentences at little listening effort for talkers speaking at a normal vocal effort level. In classrooms that are compliant with design standards, 𝐷𝐿2 provided little insight to the room’s acoustical performance. 82 Additionally, STI calculations require that the reverberation time and background noise level be known. Without measuring these quantities for each room, 𝑆𝑇𝐼 cannot be predicted accurately. As the 𝐷𝐿2 quality rating brackets are based on 𝑆𝑇𝐼, a standardized set of 𝐷𝐿2 quality ratings cannot be prescribed per room type. However, in rooms where the reverberation time and background noise levels are known and are not compliant with standards, 𝐷𝐿2 is useful in determining the distance until which speech intelligibility is acceptable. 4.4.2 Case 2 (Distraction) The sample analysis assumed that rooms where speech distraction is an issue contain seating dividers. In general, spaces where occupants intend to work without distraction either have subdivided spaces or enforce rules to limit speech levels. In situations where the evaluation distance is unknown, the model may be used to generate a series of 𝑆𝑇𝐼 vs 𝐷𝐿2 graphs to present more insight than a single graph can. In this situation, the model was also more useful as a design tool than for evaluating rooms. The graphs grant designers insight to the amount of distraction expected at varying distances from a talker and allow designers to furnish the room to meet 𝐷𝐿2 values that limit distraction to acceptable amounts. Perhaps most importantly, the model predicts that speech distraction targets are achievable with DL2 values observed in real rooms. While factors that are expected to influence 𝐷𝐿2 (such as divider density, height, and absorptivity) were not studied specifically, the model gives designers more realistic expectations for the performance of a room. 4.4.3 Case 3 (Privacy) For rooms where privacy is desired, the model predicted that speech privacy is only achievable in rooms with partial dividers when listeners are nearby. The sample setting was an eating establishment where increases in background noise levels are acceptable to promote better speech privacy. In cases where adjusting 𝐷𝐿2 alone is not sufficient to provide satisfactory amounts of speech privacy, and the nearest listener location is known, the model could also be used to evaluate the 83 level of background noise required to achieve the required amount of speech privacy. These conditions also vary by eating establishment, and designers may opt to use a combination of seating booths, greater distances between tables, and higher background noise levels if allowed by design constraints. 4.4.4 General Model Use Guideline Through the sample applications, the model was found to be best suited for design or acoustical improvement analysis as opposed to being a standardized metric. By specifying the relevant room parameters (background noise level, reverberation time, speech vocal effort level, and room dimensions), the model will generate either a 𝑆𝑇𝐼 vs 𝐷𝐿2 or 𝑆𝑇𝐼 vs distance chart. The 𝑆𝑇𝐼 vs distance chart is useful to determine, at a glance, if the 𝑆𝑇𝐼 targets for the room are being met. If 𝑆𝑇𝐼 targets are not met, users can modify the background noise level, the reverberation time, or both, to obtain the proper 𝑆𝑇𝐼 at various distances. Background noise level reduction can be achieved by proper HVAC system balancing or mitigating noise sources in a room. Conversely, background noise levels can be increased either by playing music or using a sound masking system. Reverberation time is mainly adjusted by introducing or removing acoustic absorption. Alternatively, if the room setting permits, the user may choose to investigate the installation of dividers in their space. The 𝑆𝑇𝐼 vs 𝐷𝐿2 chart lets users focus on a single, critical location to identify the 𝐷𝐿2 required to achieve the desired 𝑆𝑇𝐼 targets. The tool ultimately allows users to adjust room parameters to determine the type and extent of work required to achieve either ideal or acceptable room conditions. The user can then determine costs before committing to lengthy and possibly expensive mitigation work. 4.5 Conclusions The initial model developed in Chapter 2 was updated according to experimental observations made in Chapter 3. Additionally, by modifying the inputs to the full speech transmission index calculation scheme, sound pressure level data may be used. The full 𝑆𝑇𝐼 calculation scheme was also implemented in the 𝐷𝐿2 model. 84 The refined model was used to assess a hypothetical room of each room type. The background noise level and reverberation times were specified according to BB93 for each room. The model was used to analyze or design each room. For intelligibility cases, 𝐷𝐿2 was found to provide redundant information if the room meets recommended reverberation time and background noise levels specified in design standards. However, 𝐷𝐿2 is useful in rooms where recommended reverberation time and background noise level are not met as it allows for optimized use of a suboptimal room. In the distraction case, the model was used to produce 𝑆𝑇𝐼 vs 𝐷𝐿2 curves for a range of distances. The model recommended 𝐷𝐿2 values of greater than 6 dB/DD for productivity loss of 2% at 4 m. In rooms where dividers are present, 𝐷𝐿2 values range from 4 – 9 dB/DD. The recommended values are plausible and may be used by designers to achieve speech distraction requirement targets. In the privacy case, the model concluded that good speech privacy is not possible at small distances (e.g. 4 m) if internal dividers (e.g. booths) are absent. However, by producing 𝑆𝑇𝐼 vs 𝐷𝐿2 curves for varying levels of background noise levels, the model produced a chart of recommended 𝐷𝐿2 values to meet user-specifiable privacy targets. The model was found to be most useful in analyzing rooms as opposed to prescribing set 𝐷𝐿2 values corresponding to quality ratings. This is due to the variability of reverberation time and background noise levels from room to room. 85 5 Conclusion 𝐷𝐿2 was proposed as a universal room acoustics parameter with the intent to establish a standardized rating system. An initial model was built based on the foundation work that resulted in ISO 3382-3, which related 𝐷𝐿2 to the speech transmission index (𝑆𝑇𝐼) to facilitate specifying rating criteria. The initial model was built to calculate 𝑆𝑇𝐼 considering only reverberant speech and assumed the behavior of sound in rooms. While inherently inappropriate for rooms where direct speech is present, the model was used as a base that was to be improved using experimental data and proper 𝑆𝑇𝐼 calculation algorithms. While 𝐷𝐿2 is a parameter that is evaluated the same way regardless of room type, the rating schemes to assess room acoustic quality depend on how rooms are used. Three room use cases were identified: Case 1 (intelligibility) rooms where good speech intelligibility is desired throughout the space, Case 2 (distraction) rooms where good speech intelligibility is desired near a talker and distracts unintended recipients, and Case 3 (privacy) rooms where good speech intelligibility is desired near a talker and is meant to be confidential to nearby unintended listeners. The room type categorization helped determine appropriate rating schemes. Case 1 requires that speech be fully intelligible to the intended audience and rates rooms based on listening effort. Case 2 requires that speech be fully intelligible at short distances, and the room rating is based on the percent of productivity loss caused at unintended listener locations. Case 3 requires that speech be fully intelligible at short distances, and the room rating is based on the percentage of the sentence intelligible at unintended listener locations. The quality rating brackets were derived from existing research relating 𝑆𝑇𝐼 ratings to the impact on human listeners. Experimental data were then used to modify the initial model such that it would better reflect the behavior of sound in real world conditions. The linearity of sound decay, the sound pressure level at 1 m from a sound source, and the frequency variation of 𝐷𝐿2 were studied. It was found that 𝐷𝐿2 can be assumed to be reasonably linear if the evaluation range is limited to 16 m, the sound pressure level at 1 m in rooms is usually higher than in free-field environments, and 𝐷𝐿2 is 86 generally less in low frequency bands and higher in high frequency bands. The trends evident in the data were then implemented in the initial model. Finally, the 𝑆𝑇𝐼 calculation algorithm was modified such that it would accept the inputs available from 𝐷𝐿2 measurements, specifically the total speech sound pressure level. The modified 𝑆𝑇𝐼 calculation algorithm was then implemented, resulting in a final 𝐷𝐿2 model. The complete model was then used to evaluate hypothetical rooms for each case. The rooms were modeled based on conditions specified by standards used in acoustical engineering. The rating schemes were then applied to their respective cases. Through the sample applications, it was found that 𝐷𝐿2 is more useful as a design tool than as a standardized quality metric. To prescribe standardized quality ratings using only 𝐷𝐿2, the reverberation time and background level for each type of room will need to be assumed. Since reverberation time and background noise levels are known to vary greatly between rooms of the same type (e.g. classrooms), the same 𝐷𝐿2 value in two rooms of differing reverberation time and background noise level will produce different 𝑆𝑇𝐼 vs Distance graphs. Thus, standardized quality ratings based only on 𝐷𝐿2 are expected to have unreasonably large errors. However, if the reverberation time and background noise level are known, 𝐷𝐿2 can be used to gain deeper insight on how a room can be optimized for its intended use. 87 6 Future Work The following sections outline aspects that the authors identified as work that can be done to further improve the 𝐷𝐿2 design tool. 6.1 Speech Distraction Figure 2.6 of chapter 2, the loss of productivity versus 𝑆𝑇𝐼 curve is based on a wide variety of speech signals from foreign languages to contextual speech. In the case of typical workplaces, it is reasonable to assume that speech would be in the listener’s native language and the topics are contextualized and are of interest to the listener. It is therefore of interest to assess the loss of productivity due to conversations directly relevant to the listener. This, however, may have ethical repercussions and would be difficult to execute if the tests used speech signals that are directly relevant to the daily lives of the listeners. Given the difficulty of simulating the conversations in a typical workplace environment, the distraction curve presented in Figure 2.6 may be the best approximation at the time this thesis was completed. 6.2 Workplace Dividers In chapter 3.1.4, the effects of workplace dividers on the sound pressure level were observed. However, the data collected were not sufficient to understand how sound is diffracted, transmitted, or reflected around a divider, or how factors such as divider reflectivity, transmissivity, absorptivity, and geometry affect the sound pressure level in the immediate vicinity of a workplace divider. It is hypothesized that the distance from the previous divider and the distance to the next divider also contribute to the sound pressure level before and after the divider of interest. As the pre-existing data were not collected at sufficiently fine intervals before and after a divider for various heights, the specific effects of dividers were not included in the 𝐷𝐿2 tool. As of this thesis, the best approximation for divider effects would be to assume that the sound pressure level is 1 – 3 dB higher than the predicted sound pressure level before a divider, and 1 – 3 dB lower than the predicted sound pressure level after a divider. However, the mechanisms dictating the magnitude of the over and underestimation in the vicinity of dividers are yet unclear and warrant further investigation. 88 Works Cited [1] T. Houtgast and M. Steeneken, "Predicting Speech Intelligibility in Rooms from the Modulation Transfer Function," Acustica, vol. 16, pp. 60-72, 1980. [2] I. Sharland, Woods Practical Guide to Noise Control, Salford: Woods Acoustics, 1972. [3] E. Lindqvist, Sound Propagation in Large Factories, Gothenburg: Department of Building Acoustics, 1981. [4] M. Hodgson, "Measurement of the Influence of Fittings and Roof Pitching on the Sound Field in Panel-Roof Factories," Applied Acoustics, no. 16, pp. 369-391, 1983. [5] M. Hodgson and N. Heerema, "Sound-Propagation Curves in Industrial Workrooms: Statistical Trends and Empirical Prediction Models," Building Acoustics, vol. 3, no. 1, pp. 25-32, 1996. [6] A. Ondet and J. Barbry, "Modeling of Sound Propagation in Fitted workshops Using Ray Tracing," Journal of the Acoustical Society of America, vol. 85, no. 2, pp. 787-796, 1989. [7] A. Ondet and J. Sueur, "Development and Validation of Criterion for Assessing the Acoustic Performance of Industrial Rooms," Journal of the Acoustical Society of America, vol. 97, no. 3, pp. 1727-1731, 1995. [8] M. Hodgson, "Experimental Investigtion of the Acoustical Characteristics of University Classrooms," Journal of the Acoustical Society of America, vol. 106, no. 4, pp. 1810-1819, 1999. [9] M. Hodgson, "Empirical Prediction of Speech Levels and Reverberation in Classrooms," Building Acoustics, vol. 8, no. 1, pp. 1-14, 2001. [10] V. Keranen, P. Virjonen and V. Hongisto, "Determination of Acoustical Conditions in Open-Plan Offices: Proposal for New Measurement Method and Target Values," Act Acustica United with Acustica, vol. 95, pp. 279-290, 2009. [11] J. Keranen and V. Hongisto, "Prediction of the Spatial Decay of Speech in Open Plan Offices," Applied Acoustics, vol. 74, pp. 1315-1325, 2013. [12] Methods for Calculation of the Speech Intelligibility Index, New York: American National Standards Institute, ANSI/ASA S3.5-1997 (R2012). 89 [13] R. Watson and O. Downey, The Little Red Book of Acoustics: A Practical Guide, Sheffield: Blue Tree Acoustics, 2008. [14] L. Beranek, "Balanced noise-criterion (NCB) curves," Journal of the Acoustical Society of America, vol. 86, no. 2, pp. 650-664, 1989. [15] American Society of Heating, Refridgerating and Air-Conditioning Engineers, Inc., 2011 Ashrae Handbook, Atlanta, 2011. [16] J. Rennies and H. Schepker, "Listening Effort and Speech Intelligibility in Listening Situations Affected by Noise and Reverberation," Journal of the Acoustical Society of America, vol. 136, no. 5, pp. 2642-2653, 2014. [17] V. Hongisto, "A Model for Predicting the Effect of Speech of Varying Intelligibility on Work Performance," Indoor Air, vol. 15, pp. 458-468, 2006. [18] A. Ebissou, E. Parizet and P. Chevret, "Use of the Speech Transmission Index for the Asessment of Sound Annoyance in Open-Plan Offices," Applied Acoustics, vol. 88, pp. 90-95, 2015. [19] Standard Test Method for Measurement of Airborne Sound Attenuation between Rooms in Buildings, West Conshocken: ASTM International, E336-14 (2014). [20] "Acoustic design of schools: performance standards," 13 December 2014. [Online]. Available: https://www.gov.uk/government/publications/bb93-acoustic-design-of-schools-performance-standards. [21] B. Monson, E. Hunter and B. Story, "Horizontal directivity of low and high-frequency energy in speech and singing," The Journal of the Acoustical Society of America, no. 132, pp. 433-441, 2012. 90 Appendix B1-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 75.6 91.1 93.7 89.2 92.4 91.6 88.7 61.1 2 64.6 79.7 82.5 79.4 79.0 81.6 77.6 50.1 4 63.8 79.2 77.9 75.5 76.9 77.2 72.1 46.6 6 61.8 73.0 74.6 73.6 72.5 73.8 68.6 43.1 8 59.5 70.3 68.9 64.1 63.5 63.1 60.1 36.9 10 57.1 71.0 71.9 63.9 61.4 61.6 56.3 38.7 DL2 [dB/DD] 4.8 5.9 6.8 7.3 8.6 8.7 9.1 6.8 B1-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.5 86.1 90.8 86.4 89.2 89.4 85.4 58.0 2 69.3 82.5 79.1 78.7 76.5 79.7 77.0 48.9 5 61.9 72.3 72.1 68.2 69.7 73.2 71.5 40.2 9 55.5 71.9 71.0 64.2 67.0 68.7 64.8 38.6 14 54.2 59.6 63.4 63.7 66.3 66.1 61.9 32.8 22 51.1 52.3 51.5 52.4 59.3 60.9 57.7 23.2 DL2 [DB/DD] 4.7 7.3 7.6 6.9 5.9 6.0 6.0 7.0 B1-3 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 76.3 89.7 93.2 88.8 91.7 93.1 86.9 60.5 2 69.4 81.5 83.5 79.0 80.1 79.4 74.5 50.8 4 64.1 79.9 80.9 77.2 78.2 77.8 70.4 48.6 8 59.0 73.6 71.2 66.7 69.4 72.7 65.1 39.8 16 55.7 62.6 63.0 52.9 56.9 58.2 51.2 29.9 DL2 [DB/DD] 5.2 6.2 7.3 8.4 8.0 7.7 8.1 7.2 91 B2-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1.5 68.0 85.2 87.4 80.8 85.2 81.2 78.5 54.3 3 63.5 78.5 81.3 77.3 80.6 79.2 76.3 48.8 5.5 60.9 75.1 79.0 72.6 74.8 73.9 71.6 45.6 7.5 61.8 70.4 73.2 69.0 74.3 72.3 70.6 40.9 10.5 52.8 67.9 71.5 66.0 69.3 66.4 63.3 38.4 12 55.7 65.4 68.9 63.5 67.3 64.4 63.3 35.9 DL2 [DB/DD] 4.3 6.4 5.9 5.7 5.8 5.6 5.3 5.9 B3-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 72.6 88.5 92.1 88.0 92.6 88.2 90.7 59.6 2 69.7 83.2 85.0 80.9 84.3 82.3 80.4 52.6 4 67.6 79.2 80.8 77.0 82.7 79.9 76.7 48.8 8 58.9 75.0 76.0 70.4 75.6 73.6 69.2 43.5 12 57.5 70.4 72.4 66.0 69.7 68.3 65.0 39.4 DL2 [DB/DD] 4.5 4.8 5.3 5.9 5.9 5.2 6.8 5.4 B3-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.8 88.4 92.9 87.5 90.2 88.4 88.5 59.7 2 70.8 83.2 85.1 79.4 81.4 81.1 77.2 52.2 4 63.4 76.6 80.9 75.7 78.2 80.3 75.3 47.9 6 64.0 73.3 75.5 69.7 72.7 74.6 69.6 42.7 8 61.5 67.2 69.6 66.0 69.4 70.3 66.3 37.5 12 54.7 66.9 64.7 60.6 62.8 64.5 63.4 33.3 16 53.6 61.9 64.2 56.0 61.1 61.5 59.1 31.0 DL2 [DB/DD] 5.3 6.6 7.5 7.6 7.2 6.6 6.8 7.3 92 B4-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 75.6 91.5 92.5 88.3 93.1 89.7 86.4 60.3 2 68.7 86.2 87.4 84.1 87.9 86.0 83.2 55.4 5 64.2 79.4 80.9 76.4 77.1 76.1 73.0 48.3 9 55.6 71.2 71.7 68.1 68.8 68.3 66.8 39.5 13 51.2 68.1 67.6 60.8 62.9 60.7 57.3 35.0 16 49.9 60.7 62.1 57.0 59.5 57.9 53.7 29.5 24 48.0 57.6 57.3 53.1 58.3 55.2 52.1 25.5 DL2 [DB/DD] 6.3 7.5 7.7 8.0 8.3 8.1 8.2 7.8 B4-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 71.8 90.2 93.1 88.6 94.0 91.3 91.1 60.7 2 69.3 83.7 87.3 81.3 85.9 84.0 81.2 54.2 5 61.6 76.4 78.2 73.2 77.2 77.6 72.9 45.7 12 58.3 75.3 77.0 71.2 74.7 75.8 72.6 44.3 DL2 [DB/DD] 4.0 4.3 4.7 4.9 5.5 4.3 5.2 4.7 B4-3 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 69.2 85.7 87.9 82.7 87.3 84.4 80.9 55.2 2.5 66.9 82.2 85.5 79.7 82.7 81.5 79.6 52.4 3.5 63.2 78.1 83.0 75.8 80.5 79.1 76.7 49.5 DL2 [DB/DD] 3.0 3.9 2.5 3.5 3.7 2.8 2.0 2.9 93 B5-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 72.6 89.9 92.7 88.4 91.2 91.5 87.3 60.1 2 71.9 83.2 85.3 80.4 81.7 81.5 78.1 52.5 4 64.4 79.5 81.6 75.2 76.7 77.6 73.3 48.5 6 66.8 76.7 79.9 72.7 75.5 75.3 69.2 46.5 8 65.7 72.8 72.7 66.7 69.5 70.2 66.6 40.3 12 59.6 72.9 70.6 64.3 66.0 66.5 62.4 38.7 16 60.7 64.7 64.9 57.3 61.5 61.4 60.5 32.3 20 58.0 63.8 63.6 56.1 59.3 59.6 56.7 31.0 22 57.3 62.5 59.9 53.8 59.3 58.3 55.8 28.6 DL2 [DB/DD] 3.5 6.0 7.0 7.6 7.1 7.2 6.8 6.8 B5-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 68.6 84.8 85.8 82.2 83.6 82.9 78.9 53.6 2 72.8 82.5 84.8 81.0 81.7 83.3 80.4 52.3 4 63.1 76.4 79.9 77.7 79.1 79.3 74.9 47.8 6 67.0 75.7 78.0 74.4 75.5 75.8 71.3 45.6 9 64.0 71.0 71.6 67.6 70.9 70.2 67.8 39.6 13 59.8 67.9 68.7 65.0 65.5 66.8 63.4 36.5 15 60.0 65.2 64.4 58.9 62.5 63.7 62.1 32.5 19 59.1 65.8 62.5 57.9 62.4 62.0 59.3 31.6 DL2 [DB/DD] 2.8 4.9 5.8 6.1 5.5 5.4 5.1 5.6 B6-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.5 88.8 92.9 88.7 91.7 90.0 90.9 60.2 2 62.2 90.0 87.6 84.2 86.8 85.9 84.3 56.4 4 60.5 76.2 76.3 71.6 73.7 72.7 70.8 44.0 7 56.6 72.7 68.2 61.7 66.8 64.8 62.3 37.3 DL2 [DB/DD] 4.6 6.6 9.0 9.9 9.3 9.4 10.5 8.6 94 B6-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.5 88.8 92.9 88.7 91.7 90.0 90.9 60.2 2 66.1 82.1 83.4 79.5 80.6 79.0 76.7 51.0 4 58.3 75.3 80.3 75.4 76.7 74.9 73.7 47.1 6 59.3 73.5 76.5 69.1 71.5 70.0 67.3 43.1 8 58.0 67.1 70.1 65.2 67.4 66.2 65.4 37.2 11 53.1 65.3 69.9 62.9 64.0 61.3 59.6 36.3 14 52.9 60.7 61.8 57.6 59.7 59.6 57.0 29.5 DL2 [DB/DD] 4.6 7.1 7.3 7.8 7.9 7.8 8.3 7.4 B7-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.8 88.4 90.4 88.1 91.0 87.0 86.8 58.5 2 67.1 85.4 85.3 78.3 79.6 77.8 76.4 52.5 4 62.9 77.5 81.5 75.3 76.6 75.1 71.0 48.1 8 61.1 73.4 73.8 67.7 69.0 68.6 65.3 41.1 10 61.1 68.7 73.4 65.6 68.3 66.9 62.5 39.7 17 57.4 62.0 61.7 53.9 56.3 55.6 52.9 29.1 24 59.2 56.7 53.0 44.5 51.7 50.3 47.0 23.2 30 57.1 55.8 52.8 45.1 53.2 51.7 48.9 22.4 DL2 [DB/DD] 2.7 7.0 8.0 8.9 7.9 7.4 7.9 7.6 B7-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 75.1 88.5 91.3 86.9 90.6 89.6 86.7 58.7 2 69.8 83.1 83.6 77.7 81.0 80.4 79.3 51.0 4 65.0 76.3 81.7 74.8 76.6 74.7 73.5 48.0 6 63.1 71.5 74.4 67.8 70.5 71.1 66.2 41.2 8 60.3 72.5 72.9 66.4 68.2 70.0 64.6 40.2 10 57.4 68.8 71.1 62.1 64.3 65.9 62.3 37.6 14 57.4 63.0 64.9 55.7 58.8 58.5 55.0 31.5 18 57.8 60.4 59.7 51.3 55.4 53.7 52.1 27.4 DL2 [DB/DD] 4.5 6.6 7.1 8.1 8.2 7.9 8.2 7.1 95 B8-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.5 86.4 89.6 84.7 91.8 86.0 84.0 57.2 2 68.2 80.6 80.8 74.4 80.9 77.2 73.4 48.4 5 56.5 64.3 67.9 62.0 67.1 63.1 56.0 34.9 7 55.6 68.4 66.2 60.7 66.1 62.6 57.1 34.6 10 53.0 58.2 57.6 55.6 59.1 55.4 50.6 26.5 12 51.4 58.9 60.1 56.6 60.8 57.9 53.6 28.1 16 49.0 51.4 52.7 46.7 52.6 48.7 45.1 20.3 18 49.2 55.4 53.0 48.7 53.0 49.1 45.0 21.8 DL2 [DB/DD] 5.5 8.1 8.9 8.5 9.2 8.8 9.1 8.7 B9-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 81.5 92.3 93.2 84.3 85.7 80.0 74.8 59.9 2 73.9 91.5 87.0 80.4 81.5 76.4 68.8 55.9 4 71.1 82.5 82.6 73.4 72.5 68.0 60.2 49.5 6 62.9 79.9 78.4 67.3 66.4 63.5 55.0 45.6 9 64.9 76.5 72.2 61.8 62.2 58.9 50.7 40.8 12 59.3 69.9 70.6 58.4 58.6 53.8 46.6 37.1 DL2 [DB/DD] 5.8 6.2 6.4 7.5 7.9 7.4 8.0 6.4 B10-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.8 89.4 91.3 87.2 93.6 88.2 85.5 59.2 2 63.8 82.7 79.5 75.7 81.0 77.7 71.5 48.6 6 55.1 65.6 65.6 55.3 59.5 55.9 51.2 32.5 14.1 52.8 60.2 58.1 47.8 53.8 50.0 44.4 25.9 DL2 [DB/DD] 5.7 8.1 8.7 10.7 10.8 10.5 11.0 8.9 96 B10-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.4 91.2 93.5 89.0 92.7 90.9 86.1 60.9 2 67.3 84.2 88.4 84.7 90.5 87.5 83.0 56.2 5 64.2 75.2 77.2 73.0 75.9 74.9 70.5 44.7 8 59.0 75.4 75.0 71.8 77.1 74.3 65.5 43.5 16 56.2 62.9 62.3 54.5 59.8 57.7 51.2 29.9 32 48.1 54.8 55.4 45.8 56.8 53.2 45.6 22.9 44 43.8 48.8 45.8 39.7 51.0 49.9 41.3 15.6 DL2 [DB/DD] 5.2 7.6 8.5 9.3 8.0 8.0 8.7 8.3 B10-3 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 76.4 88.3 94.1 88.5 93.7 90.9 84.5 61.0 4 72.1 87.4 88.9 82.2 86.8 84.1 77.1 56.0 8 66.3 80.0 81.9 74.7 78.9 76.5 69.0 48.8 16 62.5 80.4 74.0 65.8 72.3 69.0 62.0 44.0 DL2 [DB/DD] 3.5 2.3 4.9 5.5 5.4 5.4 5.6 4.3 B10-4 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 2 72.9 83.9 88.7 84.8 91.0 88.8 80.9 56.4 4 68.6 80.8 80.2 75.9 79.2 77.2 69.0 48.2 8 59.2 73.5 74.0 64.7 67.4 67.3 55.8 40.8 16 53.2 63.6 62.0 50.6 56.6 54.7 46.7 29.4 20 49.0 61.5 58.5 47.7 54.7 52.6 44.1 26.6 DL2 [DB/DD] 7.2 7.1 9.0 11.5 11.1 11.0 11.2 9.0 97 B11-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 2 72.9 83.9 88.7 84.8 91.0 88.8 80.9 56.4 4 68.6 80.8 80.2 75.9 79.2 77.2 69.0 48.2 8 59.2 73.5 74.0 64.7 67.4 67.3 55.8 40.8 16 53.2 63.6 62.0 50.6 56.6 54.7 46.7 29.4 20 49.0 61.5 58.5 47.7 54.7 52.6 44.1 26.6 DL2 [DB/DD] 7.2 7.1 9.0 11.5 11.1 11.0 11.2 9.0 B11-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.4 89.2 92.7 89.8 93.2 90.6 82.3 60.5 1.5 62.3 80.2 81.2 76.6 80.7 81.6 72.9 49.0 4.1 59.7 71.9 78.5 72.3 77.9 78.3 71.7 45.3 6 58.9 68.3 68.9 63.7 71.6 70.7 62.1 37.1 8.5 52.2 68.7 69.4 59.7 65.5 64.6 55.0 36.3 DL2 [DB/DD] 4.6 6.6 7.0 8.6 7.5 7.3 7.4 7.1 B12-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 72.6 88.6 94.1 88.9 94.0 91.5 88.2 61.1 2 63.1 82.9 83.8 76.7 79.8 78.7 75.3 50.8 3.8 60.4 75.0 74.8 69.8 71.7 72.3 67.2 42.5 5.8 57.1 69.8 70.2 64.4 65.9 66.0 61.4 37.6 7.7 53.9 71.6 64.3 59.9 59.7 60.5 54.9 35.1 9.4 52.8 65.5 63.2 54.5 57.3 55.6 49.5 31.0 11.5 51.0 61.5 62.3 52.0 53.1 52.9 47.0 28.9 13.3 52.7 59.0 56.0 49.3 50.2 49.4 43.7 24.5 15.5 54.3 61.6 56.8 48.4 50.1 48.1 41.8 26.0 20 53.7 54.8 54.4 47.3 51.9 50.2 43.1 22.3 DL2 [DB/DD] 4.5 7.7 9.3 10.0 10.5 10.4 11.2 9.0 98 B12-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 73.0 86.9 92.5 88.3 94.0 91.3 84.1 59.9 2.3 68.2 81.2 82.0 75.0 80.1 76.8 73.9 49.2 6.4 62.2 69.0 74.9 64.9 69.2 65.5 59.3 40.8 8.1 64.3 63.4 62.3 59.6 66.3 60.9 56.6 32.0 11.8 59.2 61.9 60.0 51.9 55.8 53.8 47.2 28.2 13.7 60.5 57.8 54.0 46.2 52.9 49.0 44.0 24.3 18.8 58.5 55.7 54.1 44.3 50.8 47.5 41.4 23.0 20.5 58.6 51.5 48.9 39.1 42.4 42.3 35.9 20.1 25 57.0 51.0 45.7 36.4 41.9 42.2 35.9 18.5 27 59.2 48.7 45.4 36.4 39.8 40.0 33.0 19.4 30 57.3 49.3 44.9 43.5 48.9 47.6 37.8 18.8 DL2 [DB/DD] 3.1 8.2 10.1 10.6 10.8 10.2 10.6 8.8 B13-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 78.1 88.7 95.7 89.7 93.6 93.0 83.8 62.3 2 66.8 80.4 81.6 76.5 77.8 76.4 70.5 48.9 4 58.2 74.9 77.5 69.8 74.2 76.7 67.3 44.3 6 62.7 72.6 70.3 61.0 68.8 72.2 62.4 38.5 7.6 62.1 65.6 68.6 56.2 62.0 64.8 54.2 34.9 9.4 64.3 63.1 62.2 52.8 59.6 60.3 50.6 30.5 12.4 64.6 60.9 61.2 48.0 55.8 55.9 47.2 29.3 14 63.4 55.2 56.6 48.8 53.8 53.8 45.4 26.0 15.6 60.5 56.4 58.7 49.3 54.8 54.6 45.5 26.2 DL2 [DB/DD] 2.9 8.3 9.3 10.7 9.7 9.5 9.7 8.9 99 B13-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.3 90.3 95.3 90.6 92.5 92.0 84.4 62.2 2 69.3 83.7 84.3 82.1 81.8 81.5 76.3 52.5 5 60.7 76.7 81.2 74.0 76.5 77.0 69.0 47.6 6.9 61.3 71.3 71.4 71.0 72.7 75.3 67.6 40.8 9.8 53.9 64.1 67.9 60.9 64.3 67.3 56.8 34.6 11.6 53.1 63.1 63.2 55.6 60.0 59.2 51.7 30.5 DL2 [DB/DD] 5.9 7.7 8.3 9.1 8.3 7.7 8.4 8.3 B14-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 76.4 91.1 92.6 88.0 93.5 90.9 87.3 60.3 2.5 67.2 86.4 89.7 82.9 89.5 85.3 77.9 56.6 3.5 71.8 86.5 88.7 82.2 87.9 86.5 79.5 55.8 6.4 64.0 72.9 76.2 68.7 71.9 70.0 61.1 42.8 8.5 62.5 72.1 72.7 66.2 69.2 66.6 58.9 39.9 10.1 63.6 72.7 73.0 66.3 70.7 66.8 59.6 40.4 12.7 62.2 65.6 64.8 56.3 58.9 56.2 49.0 32.4 14.7 61.1 62.4 62.3 54.5 59.0 54.0 47.8 30.0 16.1 60.5 61.0 64.6 53.9 59.1 54.5 49.6 31.0 19.4 54.4 55.0 54.0 45.0 49.1 45.7 38.9 21.9 21.1 52.6 50.7 50.5 41.6 49.4 44.9 38.7 18.7 23.4 54.8 57.0 52.9 43.1 50.2 46.7 38.8 22.2 DL2 [DB/DD] 4.7 9.0 9.9 10.9 11.0 11.3 11.6 9.7 100 B14-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 75.0 90.5 92.3 89.4 95.1 90.9 86.3 60.6 3.8 62.9 83.6 86.1 78.9 87.2 82.1 76.3 53.2 5.3 67.8 75.1 75.1 71.9 74.5 71.1 64.0 43.3 9.5 61.1 72.5 74.9 69.9 74.4 71.3 63.4 42.2 12.2 59.8 70.1 64.8 57.5 62.2 56.8 50.4 34.3 14.9 59.9 71.3 68.0 58.8 63.7 59.6 54.9 36.3 19 60.3 64.1 64.6 54.9 60.0 55.9 50.2 31.7 DL2 [DB/DD] 3.6 5.9 6.9 8.3 8.7 8.6 8.9 6.9 B15-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.4 87.4 89.8 86.5 91.9 89.8 80.8 57.9 2 65.7 86.5 84.9 81.2 84.3 82.6 77.7 53.3 3.7 60.6 79.7 81.4 76.0 78.5 78.5 70.8 48.6 5.5 61.0 73.9 78.1 67.4 71.6 71.5 64.8 44.1 7.5 61.4 71.9 70.9 64.4 68.8 67.3 62.8 38.7 DL2 [DB/DD] 3.3 5.8 5.9 7.8 8.0 7.6 6.6 6.3 B15-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.7 86.1 91.3 88.0 91.2 91.0 79.8 58.8 2.9 70.5 80.7 82.5 80.2 84.3 83.3 73.0 50.9 4.7 62.4 74.9 79.5 77.7 79.7 81.1 70.2 47.6 8 60.2 75.9 74.8 69.3 75.8 74.2 62.3 43.0 9.7 59.2 70.6 73.2 68.2 73.5 73.6 62.6 40.7 14.4 56.7 65.3 68.6 61.2 68.6 68.2 56.2 35.6 DL2 [DB/DD] 5.0 5.0 5.7 6.8 5.7 5.8 6.0 5.8 101 B16-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 77.6 88.4 94.4 89.8 94.3 91.8 88.5 61.5 1.9 68.3 79.9 86.0 80.2 85.4 82.7 77.8 52.8 3.2 66.2 75.9 81.1 76.2 81.3 79.9 73.3 48.3 5.2 62.9 72.5 76.2 73.3 78.0 75.3 71.6 44.2 8.6 58.8 67.9 70.2 65.0 70.8 68.8 63.6 37.7 9.9 58.6 69.0 69.0 63.2 70.9 67.7 64.1 37.0 11.9 54.5 63.9 65.4 57.0 65.7 63.2 57.7 32.6 13.5 55.7 63.4 63.9 56.7 66.4 63.9 58.6 31.8 15.5 53.6 61.0 59.9 54.1 61.9 60.2 54.7 28.3 16.8 55.3 59.3 58.9 53.9 61.4 58.7 53.6 27.4 DL2 [DB/DD] 5.4 6.5 8.4 8.8 7.7 7.7 8.0 8.1 B16-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.9 89.4 94.9 88.3 94.8 92.3 91.1 61.7 2.6 67.3 80.2 87.1 81.1 86.6 84.3 79.5 53.8 4.5 64.8 72.7 75.0 69.6 76.3 76.9 71.5 42.7 7.4 56.6 76.6 73.5 68.5 73.7 71.8 67.7 42.3 9.1 56.8 71.0 68.9 59.1 66.4 66.8 62.0 36.8 11.6 57.4 68.7 64.8 55.6 62.9 63.4 57.6 33.5 DL2 [DB/DD] 5.5 5.4 8.5 9.2 9.0 8.2 9.2 7.9 102 B17-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.5 91.2 91.4 88.0 94.6 87.9 84.6 59.9 4.3 58.6 76.1 77.3 69.6 76.2 70.4 67.2 44.4 6.2 54.4 72.2 72.0 65.0 75.8 68.0 64.7 40.1 8 53.4 74.2 74.1 67.5 73.8 68.0 64.8 41.7 11.5 51.8 63.3 63.7 56.4 63.3 56.6 53.5 31.1 13.5 51.4 63.0 68.4 56.4 64.2 58.4 54.7 34.3 15.4 51.5 57.3 57.8 50.6 60.9 55.5 54.0 25.8 17.3 53.4 58.8 59.9 52.2 61.7 57.3 54.1 27.5 24 52.3 53.7 56.1 50.2 62.9 58.7 54.1 25.1 DL2 [DB/DD] 4.9 8.3 7.8 8.7 7.7 7.2 7.3 7.9 B17-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 77.5 89.0 93.0 88.4 95.5 87.7 85.1 60.6 2.6 64.0 84.7 89.1 81.0 90.3 83.4 80.6 55.9 4.4 60.5 74.8 78.0 70.3 75.8 70.7 65.8 44.6 7.1 55.7 70.7 70.5 68.5 73.5 66.4 64.3 39.3 9 56.9 71.8 74.0 65.6 72.0 65.5 61.6 40.7 11.7 53.5 68.3 69.3 63.5 67.9 61.9 58.6 36.6 13.6 54.1 67.3 64.4 60.3 67.7 62.0 57.1 33.6 16.3 54.0 63.1 63.9 58.9 69.3 60.5 55.5 32.5 DL2 [DB/DD] 5.7 6.3 7.7 7.4 7.5 7.4 7.8 7.3 B17-3 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.6 92.1 92.0 88.0 93.1 89.2 82.3 60.1 4.9 63.4 78.1 79.5 75.0 77.2 74.4 69.6 46.9 6.9 59.6 71.3 72.8 69.4 73.5 71.8 68.1 40.8 10.5 57.0 67.3 67.3 64.4 68.2 65.5 62.0 35.7 12.4 57.1 68.1 69.1 61.9 67.1 64.4 59.1 36.3 15.5 59.7 63.0 65.4 57.1 66.1 63.0 57.2 32.6 DL2 [DB/DD] 4.4 7.2 6.8 7.6 7.1 6.8 6.3 7.0 103 B17-4 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.6 88.0 92.0 88.1 93.6 88.7 86.1 59.6 2.9 64.1 79.1 82.7 76.6 80.2 74.5 72.0 49.5 6.1 64.9 77.9 75.4 73.9 77.2 72.9 69.7 44.8 8.4 55.9 68.6 70.9 62.5 66.3 61.8 57.6 37.5 12 57.6 69.8 71.3 62.0 65.9 62.1 58.7 37.9 13.8 58.3 64.5 65.0 56.0 62.1 57.8 53.8 32.1 17.5 57.1 61.3 62.5 54.8 62.0 57.7 52.8 29.8 DL2 [DB/DD] 4.2 6.1 6.9 8.1 7.9 7.6 8.1 7.0 B18-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 67.4 89.2 89.3 83.0 82.7 77.3 71.7 56.5 2 63.4 79.3 80.0 74.0 74.6 70.0 61.9 47.1 4.5 59.9 76.8 76.3 69.0 68.5 64.3 57.6 43.5 7.6 56.5 70.8 68.9 62.2 62.3 57.9 50.5 36.7 11.9 48.8 66.4 62.8 54.4 54.4 50.9 41.9 31.1 16.2 47.5 61.7 59.1 48.1 48.1 44.6 35.6 26.8 20.5 42.9 60.5 55.2 45.0 46.5 41.9 32.2 24.3 24.8 40.6 54.7 53.1 41.1 43.7 38.8 31.6 20.4 DL2 [DB/DD] 5.8 6.7 7.7 8.9 8.5 8.3 8.9 7.4 B18-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 65.4 86.9 87.4 82.9 82.2 77.8 70.9 54.9 2 64.6 81.0 78.4 70.2 71.8 64.4 59.8 46.3 5 59.3 68.5 71.7 66.0 66.0 60.3 56.0 38.5 9 57.5 63.5 62.3 57.3 59.4 58.5 50.3 30.4 13 49.5 59.5 58.6 52.8 54.2 50.3 41.2 26.3 16 50.2 57.2 55.1 49.9 52.0 49.4 40.1 23.4 DL2 [DB/DD] 4.1 7.6 7.8 7.7 7.2 6.3 7.2 7.7 104 B18-3 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 67.4 89.2 89.3 83.0 82.7 77.3 71.7 56.5 2 63.4 79.3 80.0 74.0 74.6 70.0 61.9 47.1 4.5 59.9 76.8 76.3 69.0 68.5 64.3 57.6 43.5 7.6 56.5 70.8 68.9 62.2 62.3 57.9 50.5 36.7 11.9 48.8 66.4 62.8 54.4 54.4 50.9 41.9 31.1 16.2 47.5 61.7 59.1 48.1 48.1 44.6 35.6 26.8 20.5 42.9 60.5 55.2 45.0 46.5 41.9 32.2 24.3 24.8 40.6 54.7 53.1 41.1 43.7 38.8 31.6 20.4 DL2 [DB/DD] 5.8 6.7 7.7 8.9 8.5 8.3 8.9 7.4 B18-4 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.5 84.6 85.7 80.4 81.3 73.2 69.7 52.9 1.6 66.3 78.2 77.1 70.7 68.4 64.2 54.9 44.6 2.7 63.5 77.7 81.2 72.6 72.6 66.5 60.3 47.4 4.3 57.7 76.6 73.9 69.6 66.2 60.7 52.1 42.3 5.4 58.7 72.0 73.2 67.1 66.3 61.6 55.8 40.2 7.2 57.6 69.7 69.1 60.8 59.9 57.7 48.5 36.3 7.9 58.2 69.8 67.9 63.3 63.5 60.6 53.7 36.1 DL2 [DB/DD] 4.4 4.6 5.2 5.3 5.4 4.1 4.8 5.1 B18-5 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 69.9 85.1 89.2 82.4 82.9 77.2 69.8 55.6 2 66.3 78.4 78.6 74.9 73.2 69.4 64.7 46.3 4 58.7 75.5 75.8 68.5 69.2 66.4 61.0 42.8 6 58.3 71.6 72.5 66.2 68.0 63.2 56.7 39.6 7.5 58.0 71.3 71.2 64.5 65.6 59.6 56.1 38.5 DL2 [DB/DD] 4.5 4.7 5.8 6.1 5.5 5.5 4.8 5.7 105 B19 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 75.5 92.8 94.1 87.0 86.5 79.9 78.3 60.9 2 67.4 86.9 83.3 72.8 74.2 66.6 64.7 51.5 4.9 64.8 79.3 80.1 69.8 69.0 63.3 58.9 46.7 8.5 54.8 70.3 69.0 58.7 57.6 51.7 47.7 36.2 10.6 54.7 66.3 64.4 52.4 52.9 48.4 41.6 31.8 13.6 52.0 67.7 63.7 52.6 56.2 49.9 45.2 32.1 16 46.8 59.6 57.9 47.0 48.4 44.6 38.5 25.3 19.2 44.8 63.4 55.0 45.7 49.2 44.4 38.2 26.2 21.2 45.4 57.2 53.8 44.4 48.4 45.7 37.0 22.1 DL2 [DB/DD] 6.9 7.9 8.9 9.4 8.6 7.9 9.2 8.5 B20-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 73.9 91.0 91.9 91.8 93.9 91.8 82.4 61.1 4 60.3 82.1 86.7 84.1 87.5 84.3 75.2 54.5 6 64.0 79.8 85.1 83.2 86.7 84.0 74.4 53.2 8 62.3 79.9 83.9 83.1 85.9 82.6 72.2 52.5 10 60.9 75.6 82.6 81.0 85.8 82.2 72.3 50.9 12 58.3 78.6 81.2 81.0 84.1 81.5 70.9 50.3 16 57.5 76.7 80.6 79.3 82.9 80.7 69.3 49.1 DL2 [DB/DD] 3.8 3.7 2.9 3.0 2.6 2.7 3.2 3.0 106 B20-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 70.2 89.8 93.5 91.2 91.9 88.7 84.0 61.2 2 63.6 84.4 85.2 79.7 81.6 77.6 66.8 52.5 4 57.6 78.6 82.0 76.0 77.2 74.5 65.4 48.7 6 59.0 79.0 80.2 73.7 74.6 71.7 61.2 47.2 8 58.6 77.2 74.9 69.9 72.6 70.3 60.3 43.2 10 57.2 72.7 73.3 67.7 69.1 68.7 60.4 40.6 13 54.3 68.2 71.5 65.9 68.6 63.8 56.1 38.4 16 50.8 64.2 68.4 63.3 65.6 62.0 55.0 35.3 19 55.9 64.1 66.5 62.5 64.3 61.0 55.2 33.9 21 52.7 64.2 65.3 62.4 64.2 62.5 54.4 33.3 DL2 [DB/DD] 3.6 6.1 6.2 6.3 6.0 5.8 5.8 6.2 B21-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 74.0 89.3 92.2 89.9 92.8 89.4 84.2 60.2 2 69.7 88.4 89.0 87.3 89.8 87.3 82.5 57.6 4 67.2 82.9 87.7 84.5 87.9 85.7 79.7 55.3 8 61.8 80.7 85.1 80.9 84.1 82.5 75.6 52.3 12 63.8 79.0 83.7 79.8 83.0 79.1 73.1 51.0 DL2 [DB/DD] 3.2 3.1 2.3 2.9 2.8 2.7 3.1 2.6 B21-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 71.0 88.7 93.6 88.8 91.7 89.6 82.0 60.6 2 68.3 85.2 89.2 84.5 87.6 85.3 78.1 56.3 4 68.3 84.6 85.6 81.7 85.0 82.5 75.2 53.4 8 65.4 83.9 83.2 79.1 81.3 79.5 71.6 51.2 16 60.2 77.2 80.9 74.1 78.5 74.8 67.8 47.6 DL2 [DB/DD] 2.5 2.4 3.1 3.5 3.3 3.5 3.5 3.1 107 B22-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 81.8 94.0 97.0 90.2 87.6 87.3 85.8 63.5 1 77.2 90.3 91.6 85.1 83.6 79.6 76.9 58.5 2 73.3 88.8 88.9 83.5 81.8 76.8 72.2 56.2 4 72.8 84.1 89.2 82.5 80.1 76.0 69.9 55.5 6 73.8 87.1 89.4 82.4 80.3 75.4 69.1 56.0 DL2 [DB/DD] 2.3 2.3 2.0 2.0 2.0 3.1 4.5 2.0 B22-2-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 79.4 91.9 96.2 89.0 86.8 82.8 77.7 62.5 1 75.0 90.2 91.8 85.8 83.2 80.5 71.2 58.7 2 73.8 91.2 91.6 84.3 83.3 78.0 68.9 58.6 4 74.9 89.1 89.4 83.4 81.8 76.4 67.4 56.6 DL2 [DB/DD] 1.5 0.7 2.1 1.8 1.5 2.2 3.3 1.8 B22-2-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 83.5 96.8 99.7 92.1 89.6 83.8 81.0 66.1 1 78.8 90.3 94.9 87.4 85.2 79.4 75.8 61.1 2 73.2 88.8 90.7 85.1 83.5 78.0 71.6 57.6 4 70.8 87.3 88.9 83.8 81.7 75.7 68.9 56.0 6 70.3 87.0 90.0 83.6 80.9 74.7 67.7 56.5 8 72.2 88.7 90.0 82.5 81.2 74.6 67.0 56.7 DL2 [DB/DD] 3.1 2.0 2.4 2.2 2.0 2.2 3.4 2.3 108 B22-3-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 82.3 94.7 98.0 91.3 87.8 82.5 78.6 64.5 1 79.8 93.0 92.3 87.5 85.8 79.4 75.3 60.0 2 76.5 90.0 92.8 85.2 84.2 79.2 72.0 59.2 4 63.6 81.5 82.8 77.8 75.3 69.5 59.7 49.9 7 62.7 79.3 82.4 76.6 74.8 68.8 59.0 49.1 10.2 58.6 74.6 78.1 73.3 69.5 64.0 53.4 44.9 13 57.8 75.3 76.9 70.7 69.4 63.7 52.8 43.8 13.3 54.1 71.6 74.6 68.9 66.1 60.4 49.0 41.3 20 52.3 70.7 72.9 67.2 65.4 59.9 48.1 39.7 22.4 50.6 66.3 71.3 65.1 62.5 56.8 44.8 37.6 25.2 51.5 67.7 70.2 64.0 62.0 56.3 44.2 36.9 28.5 47.4 64.9 68.9 63.0 60.9 55.6 42.7 35.4 31 43.6 63.4 67.8 61.5 59.8 53.5 41.0 34.2 35 44.8 61.5 67.1 61.6 58.9 53.3 41.3 33.5 DL2 [DB/DD] 6.4 5.6 5.1 5.1 5.0 5.0 6.5 5.2 B22-3-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 80.5 93.9 97.8 90.6 89.8 86.1 77.5 64.1 1 77.0 89.2 91.1 83.3 83.3 78.5 70.6 57.7 2 74.3 89.2 91.4 83.9 82.2 78.3 71.4 57.9 4 73.0 86.1 86.6 82.1 80.0 75.0 67.9 54.0 7 69.6 84.4 86.4 79.0 77.5 72.6 63.9 53.0 10.2 66.6 81.6 82.6 76.9 75.1 70.3 62.5 49.7 13 63.9 79.9 81.3 76.0 74.0 69.2 59.6 48.4 13.3 65.2 78.9 80.0 73.5 72.6 67.3 57.8 46.9 20 62.2 74.0 78.6 72.4 71.0 64.8 56.2 45.0 22.4 62.5 75.6 78.2 71.4 69.7 63.9 54.5 44.8 25.2 59.6 74.3 75.2 69.2 68.2 62.9 52.1 42.3 28.5 59.0 71.9 73.8 67.8 66.3 60.8 50.9 40.6 31 58.2 71.0 72.7 67.1 65.1 60.6 49.1 39.7 35 56.6 70.6 72.3 66.4 64.2 59.5 48.4 39.2 DL2 [DB/DD] 3.8 3.8 3.9 3.6 3.8 4.0 4.5 3.8 109 B22-3-3 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 81.0 93.5 97.2 90.0 89.2 86.2 77.3 63.6 1 76.4 92.8 92.4 85.6 84.8 80.9 72.0 59.7 2 76.7 92.3 91.1 84.9 83.0 79.8 70.9 58.7 4 67.6 83.8 83.6 77.0 75.4 70.0 60.0 50.8 7 66.6 81.9 83.9 77.5 75.8 70.8 61.4 50.6 10.2 57.4 76.9 77.9 71.2 69.4 64.2 52.9 44.8 13 62.5 75.9 78.7 72.3 70.7 66.1 55.4 45.3 13.3 56.4 71.3 72.9 66.8 64.4 59.1 47.5 39.8 20 55.6 71.3 74.8 67.9 64.9 59.7 48.7 41.2 22.4 50.2 68.5 70.1 64.0 60.4 55.2 42.5 36.9 25.2 51.4 66.9 70.2 63.9 62.6 57.5 44.2 36.8 28.5 46.3 65.8 68.4 61.5 58.5 53.0 40.3 34.9 31 48.1 64.4 68.9 61.8 58.9 54.5 41.7 35.1 35 43.9 61.3 66.7 60.4 57.3 51.5 39.2 33.0 DL2 [DB/DD] 6.0 5.5 5.0 4.9 5.3 5.6 6.4 5.1 B22-4-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 83.4 96.0 99.2 92.1 92.7 88.9 80.6 65.7 1 75.5 92.7 90.5 86.7 84.6 81.0 73.1 58.8 2 75.9 88.6 90.4 83.1 82.2 78.1 68.7 57.1 4 75.8 87.6 88.6 81.3 79.7 74.7 65.9 55.4 6 73.5 87.0 85.6 81.4 79.2 74.0 64.6 53.6 8 72.2 84.6 87.2 80.7 78.8 73.3 64.1 53.8 DL2 [DB/DD] 2.2 2.6 2.8 2.7 3.2 3.7 4.0 2.7 110 B22-4-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 84.4 98.0 100.0 92.5 88.7 89.9 86.0 66.6 1 74.8 91.6 93.3 85.7 84.7 79.9 76.6 59.9 2 73.1 89.2 89.3 82.9 81.5 75.5 69.0 56.5 4 74.3 87.7 88.2 80.9 79.7 73.2 65.5 55.1 6 72.6 87.4 87.3 80.3 78.1 72.1 64.9 54.4 8 75.6 83.5 86.7 80.3 78.9 72.2 64.2 53.3 DL2 [DB/DD] 1.9 3.0 3.1 2.9 2.5 4.1 5.3 3.0 B22-4-3 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 80.7 92.9 98.6 90.4 88.1 84.1 81.5 64.6 1 79.4 93.2 98.2 86.6 88.6 81.5 78.1 63.9 2 74.0 89.2 92.0 85.2 82.4 78.0 72.9 58.5 4 73.1 85.4 87.7 81.2 81.4 74.4 68.4 54.4 6 72.6 86.1 87.4 80.8 79.2 72.8 64.8 54.3 8 70.0 86.5 87.8 80.6 79.0 72.7 64.0 54.6 DL2 [DB/DD] 2.6 2.1 3.3 2.5 2.6 3.1 4.6 3.0 B22-4-4 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 80.7 94.6 96.5 89.9 88.7 85.4 75.2 63.2 1 76.9 91.1 92.8 85.9 84.7 79.7 71.9 59.5 2 74.5 90.7 90.0 84.4 81.8 75.1 67.8 57.5 4 73.5 87.7 88.1 80.9 79.4 72.7 64.3 55.1 6 71.9 87.1 87.0 79.9 77.5 72.3 62.6 54.1 DL2 [DB/DD] 2.3 2.0 2.6 2.7 3.0 3.7 3.6 2.5 111 B22-5-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 83.2 96.9 99.2 92.3 91.3 84.5 77.8 65.8 1 74.0 90.7 94.4 85.8 83.7 77.6 72.6 60.5 2 70.8 86.8 88.9 80.2 78.3 74.8 67.5 55.3 4 68.8 82.6 83.4 76.5 75.9 72.0 63.3 50.3 6 66.7 82.0 80.4 75.9 73.2 68.4 62.1 48.4 8 62.9 78.0 78.9 73.6 71.4 66.5 58.6 46.1 DL2 [DB/DD] 4.4 4.3 5.2 4.5 4.7 4.2 4.6 4.9 B22-5-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 0.5 80.8 94.4 98.1 90.6 87.6 82.2 78.4 64.4 1 73.3 89.2 91.9 84.6 84.0 77.8 74.2 58.4 2 73.6 86.9 89.0 80.9 78.1 73.2 69.0 55.5 4 72.1 84.3 86.1 80.1 78.8 72.0 68.2 53.0 DL2 [DB/DD] 2.6 3.3 3.9 3.5 3.2 3.5 3.6 3.7 B22-6-1 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 73.3 90.3 92.1 84.6 83.3 79.7 71.4 58.7 2 71.0 87.7 87.7 81.3 80.1 75.4 67.6 54.9 4 69.5 84.8 86.3 79.2 77.8 73.9 65.2 53.0 8 66.5 85.5 83.9 78.6 76.4 71.3 62.8 51.7 16 61.3 79.5 80.7 75.9 74.4 68.7 59.1 47.9 DL2 [DB/DD] 2.9 2.4 2.7 2.0 2.2 2.6 2.9 2.5 112 B22-6-2 Distance [m] 125 Hz [dB] 250 Hz [dB] 500 Hz [dB] 1000 Hz [dB] 2000 Hz [dB] 4000 Hz [dB] 8000 Hz [dB] Lp,s,A [dB] 1 73.1 89.9 92 84.3 83.2 79.2 71.2 58.5 2 68.4 85.9 88.6 81.5 80.7 75.3 67.8 55.1 4 67 83.4 86.7 79.2 78.3 73.8 65.4 53.1 8 67.1 85.1 84.1 77.6 76.4 71.5 62.2 51.6 16 63.9 79.8 82.1 74.8 73.7 68.2 58.7 48.7 DL2 [DB/DD] 2.0 2.1 2.4 2.3 2.3 2.6 3.1 2.3
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Investigating sound decrement per doubling of distance as a universal room acoustics parameter
Text
Dataset