UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Investigation of factors affecting the performance of roadside noise barriers Daltrop, Shira Nicole Jones 2011-12-31

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
ubc_2011_fall_daltrop_shira.pdf [ 7.87MB ]
Metadata
JSON: 1.0072221.json
JSON-LD: 1.0072221+ld.json
RDF/XML (Pretty): 1.0072221.xml
RDF/JSON: 1.0072221+rdf.json
Turtle: 1.0072221+rdf-turtle.txt
N-Triples: 1.0072221+rdf-ntriples.txt
Original Record: 1.0072221 +original-record.json
Full Text
1.0072221.txt
Citation
1.0072221.ris

Full Text

Investigation of Factors A ecting the Performance of Roadside Noise Barriers by Shira Daltrop B.Sc., The University of British Columbia, 2009 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) September 2011 c Shira Daltrop 2011Abstract Roadside noise barriers are used to prevent tra c noise from reaching nearby residences. Two factors that may a ect the acoustical performance of highway noise barriers | sur- face absorption and nearby vegetation | were investigated. Three experimental techniques were used: full-scale laboratory tests,  eld tests, and scale-model tests. Tests with a 1.2 m high barrier on a hard surface were performed in an anechoic chamber, using source and receiver positions corresponding to di erent di raction angles. Absorption was added to the wall in various con gurations and the change in insertion loss (IL) was measured. IL’s of 12-18 dBA behind and -1 dBA in front of the re ective wall were found. Surface absorption increased IL by up to 2 dBA behind the barrier and 1 dBA in front. For the  eld tests, tra c noise was measured behind re ective noise walls without and with nearby foliage. E ects were small, less than 5 dB, but suggest that vegetation can either attenuate sound, increasing the IL, or scatter sound into the barrier shadow zone, decreasing the IL. A 1:31.5 scale-model highway con guration was created and tested in an anechoic cham- ber. Scale-model materials were chosen by performing excess attenuation measurements and doing a best  t using  ow resistivity. Absorption was tested on single and parallel noise barriers of varying heights, allowing for a comparison between adding absorption and increasing the height. Foliage tests were performed on single and parallel barriers with var- ious con gurations of model trees. Barrier absorption prevented the ampli cation of sound between parallel barriers and adding absorption was equivalent to increasing the height by 0.33 m. The foliage test results were similar to the  eld tests; the e ects were small and dependent on frequency and the size of the foliage. Predicting these results was attempted using ray tracing, the method of images (MOI), and  nite element methods (FEM). An existing ray tracing model, PRAY, was modi ed and used; however the predicted ILs were 10-30 dB greater than those measured. FEM gave IL’s 2-8 dB lower and MOI gave IL’s 5-20 dB lower than measurements. iiTable of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Theoretical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 The Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 The Decibel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Surface Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Outdoor Sound Propagation . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Noise Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Literature Review and Objectives . . . . . . . . . . . . . . . . . . . . . . . 14 3.1 Absorptive Noise Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Tree Foliage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.1 Sound Propagation Through Foliage . . . . . . . . . . . . . . . . . 18 3.2.2 Foliage and Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . 20 iiiTable of Contents 4 Full-Scale Laboratory Testing . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1 Absorption Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1.1 Spherical Decoupling Method . . . . . . . . . . . . . . . . . . . . . 23 4.1.2 Impedance Tube Method . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3 Absorptive Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.4.1 Acoustic Ba es . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.4.2 Commercial Absorbent Barriers . . . . . . . . . . . . . . . . . . . . 34 4.4.3 Soft Ground E ects . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5 Field Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.1 Tra c Noise Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.2 Ladner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.3 Nanaimo Parkway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.4 Highway 1 and Helmcken Road . . . . . . . . . . . . . . . . . . . . . . . . 48 5.5 Highway 17 and McKenzie Avenue . . . . . . . . . . . . . . . . . . . . . . 51 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6 Scale-Model Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.2 Theoretical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2.1 Air Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.2.2 Excess Attenuation Prediction . . . . . . . . . . . . . . . . . . . . 59 6.3 Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.3.1 Air-Jet Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 ivTable of Contents 6.3.2 Frequency Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.3.3 Excess Attenuation Measurements . . . . . . . . . . . . . . . . . . 67 6.3.4 Scale-Model Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.3.5 Insertion Loss Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 7.1 Edge Di raction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 7.2 Ray Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.3 Method of Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7.4 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.5.1 Full-Scale Laboratory Testing . . . . . . . . . . . . . . . . . . . . . 89 7.5.2 Foliage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 8.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Appendices A Di raction Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 A.1 Uniform Theory of Di raction . . . . . . . . . . . . . . . . . . . . . . . . 111 A.2 Svensson’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 B Creation of Finite Element Mesh . . . . . . . . . . . . . . . . . . . . . . . 118 vList of Tables 5.1 Un- and A-weighted Leq’s from three sites and above the noise wall along Highway 17 in Ladner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.2 Un- and A-weighted Leq’s from three sites and above the noise wall along Highway 17 in Ladner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.3 Un- and A-weighted Leq’s from the three sites and above the noise wall along Nanaimo Parkway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.4 Un- and A-weighted Leq’s from the three sites and above the noise wall along Helmcken Road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.5 Un- and A-weighted Leq’s from the two sites along McKenzie Avenue . . . 52 6.1 E ective  ow resistivities for full-scale materials . . . . . . . . . . . . . . . 68 6.2 E ective  ow resistivities for scale-model materials . . . . . . . . . . . . . 71 7.1 Ground re ection coe cients used for prediction . . . . . . . . . . . . . . . 94 viList of Figures 2.1 Sound propagation between a source and receiver over a surface . . . . . . 10 2.2 A-weighted tra c-noise spectrum . . . . . . . . . . . . . . . . . . . . . . . 12 4.1 Spherical decoupling method geometry . . . . . . . . . . . . . . . . . . . . 23 4.2 Re ective barrier in the anechoic chamber . . . . . . . . . . . . . . . . . . 26 4.3 Experimental setup, with source and receiver positions . . . . . . . . . . . 27 4.4 Commercial absorbent materials on the barrier . . . . . . . . . . . . . . . . 28 4.5 Random-incidence absorption coe cients of absorptive materials . . . . . . 29 4.6 Half of the re ective wall covered in the acoustic ba es . . . . . . . . . . . 30 4.7 Measured IL for di erent ba e con gurations . . . . . . . . . . . . . . . . 31 4.8 Measured A-weighted IL’s at the source-side receiver positions, for di erent ba e con gurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.9 Measured A-weighted IL’s on the non-source side of the barrier for di erent ba e con gurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.10 Measured A-weighted IL’s on the non-source side of the barrier for the three absorptive materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.11 Measured IL’s for di erent Durisol con gurations on soft ground . . . . . . 37 5.1 Average Leq and variation (2 ) from all 5 min intervals over a 30 min period 40 5.2 Three test sites in Ladner . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.3 Leq averaged over 30 minutes from three locations in Ladner . . . . . . . . 42 5.4 Three test sites in Ladner . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 viiList of Figures 5.5 Leq averaged over 30 minutes from three locations in Ladner . . . . . . . . 44 5.6 Leq averaged over 30 minutes for two barrier-receiver distances in the back- yard of 5122 59A St . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.7 Three test sites along Nanaimo Parkway . . . . . . . . . . . . . . . . . . . 47 5.8 Leq averaged over 30 minutes from three locations along Nanaimo Parkway 47 5.9 Leq averaged over 30 minutes for two receiver heights at site N1 . . . . . . 48 5.10 Three test sites along Helmcken Road . . . . . . . . . . . . . . . . . . . . . 50 5.11 Leq averaged over 30 minutes from three locations near Helmcken Road . . 50 5.12 Leq averaged over 30 minutes for two receiver heights at site V1 . . . . . . 51 5.13 Barrier on Vancouver Island with and without vines . . . . . . . . . . . . . 52 5.14 Leq averaged over 30 minutes from the vine and no vine locations at the McKenzie Avenue site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 6.1 Air-jet source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.2 Sound pressure level measured with and without the protection grid . . . . 65 6.3 Sound power level of the air-jet source . . . . . . . . . . . . . . . . . . . . 66 6.4 Sound pressure level of the air-jet, varying with source inclination angle and frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.5 Excess attenuation measurements and best- t predictions for candidate model materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.6 Excess attenuation measurements and best- t predictions for candidate model materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.7 E ective absorption coe cient of the fuzzy blanket . . . . . . . . . . . . . 71 6.8 Scale-model tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.9 Evergreen hedge along Wolfson Field . . . . . . . . . . . . . . . . . . . . . 73 6.10 Measured IL’s of a full-scale hedge and a single row of scale-model trees . . 74 6.11 Parallel-barrier scale-model con guration . . . . . . . . . . . . . . . . . . . 75 viiiList of Figures 6.12 Experimental setup of the scale model in the anechoic chamber . . . . . . . 75 6.13 Measured IL for the 5 m high re ective parallel barriers . . . . . . . . . . . 76 6.14 Measured di erence in IL between re ective parallel barriers and the other con gurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.15 Measured A-weighted IL’s for the 5 m tall barriers at the eight receiver positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.16 Measured A-weighted IL’s for absorptive and re ective parallel barriers for the three di erent receiver heights . . . . . . . . . . . . . . . . . . . . . . . 78 6.17 Measured change in IL in the case of parallel barriers with and without a line of trees along the source sides of the barriers . . . . . . . . . . . . . . 79 6.18 Measured A-weighted IL’s for the 5 m tall barriers, with and without a line of trees along the source sides of the barriers . . . . . . . . . . . . . . . . . 80 6.19 Taller, denser foliage behind the barrier . . . . . . . . . . . . . . . . . . . . 81 6.20 Measured change in IL between a re ective barrier and the di erent foliage con gurations with shorter trees . . . . . . . . . . . . . . . . . . . . . . . . 82 6.21 Measured change in IL between a re ective barrier and the di erent foliage con gurations with taller trees . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.1 Four sound paths between a source and receiver with a barrier in between . 87 7.2 Anechoic chamber test con guration for prediction . . . . . . . . . . . . . 89 7.3 Measured and predicted 1000 Hz sound pressure levels of the no barrier case in the anechoic chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.4 Measured and predicted 1000 Hz IL’s of the wall built in the anechoic chamber 91 7.5 Measured and predicted change in IL due to absorption on a barrier at 1000 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.6 Measured and the best- t predicted SPL to determine the ground re ection coe cient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 ixList of Figures 7.7 IL of a row of trees, comparing results from ray tracing and scale-model measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 A.1 A di racting edge, with parameters as de ned for the UTD formulation . . 111 A.2 A di racting edge, with parameters as de ned for Svensson’s model . . . . 113 A.3 Zones around a di racting edge . . . . . . . . . . . . . . . . . . . . . . . . 115 xAcknowledgements I would like to thank my supervisor Dr. Murray Hodgson for his constant guidance and support. I would also like to thank Chris Bibby, Benjamin Collin, Maureen Connelly and Behrooz Yousefzadeh for their help with  eld tests and for sharing their knowledge. Additionally, I would like to thank Clair Wake eld for contributing his experience and knowledge of tra c noise to this project. I’d also like to thank Armtec and Retaining Walls Northwest for supplying the commercial absorbent noise barriers for testing. Finally I would like to thank the British Columbia Ministry of Transportation and Infrastructure for funding this research. xiChapter 1 Introduction Tra c noise is a big problem for residents living near main roads and highways. Excessive noise can drastically impair residents’ ability to communicate, concentrate and sleep, and therefore e ective noise control in these situations is crucial. Much work goes into the mitigation of such noise; governments or consultants responsible for this mitigation look for ways to increase the e ectiveness without greatly increasing the cost. One common method of noise control is the use of roadside noise barriers; they block the direct sound path between the source | the tra c | and the receiver | the person or household subject to the noise. These barriers can be walls, earth berms, or walls on top of earth berms. The topic of study here is noise walls, which are typically made of concrete to ensure little to no sound is transmitted, as well as ensuring durability. While one way to increase the e ectiveness of a noise wall is to increase the height, there is a maximum acceptable height in most places; in British Columbia this limit is currently 3 m [1]. This is in place to limit the visual impact for both the drivers and the residents as well as to control costs. While earth berms avoid this visual impact and therefore do not have a height limit, there are many cases where berms are not feasible, either because of geographical topography or a lack of adequate space. Therefore, means of obtaining greater noise reductions from noise walls is a topic of much investigation. Acoustical consultant Clair Wake eld and the British Columbia Ministry of Transportation and Infrastructure wish to gain more knowledge on several factors which a ect the performance of these noise walls, and therefore the ministry has funded this research project. 1Chapter 1. Introduction Concrete noise barriers are typically sound re ective; therefore sound can re ect back from them and increase noise levels on the source side of a barrier. In the case of parallel barriers, when barriers are on either side of a road or highway, re ected sound will amplify the noise between the barriers. The sound level at each barrier will therefore increase and more sound will reach the opposite sides of the barriers. Therefore, the barriers become less e ective. One way to avoid this degradation is to make the barriers out of sound ab- sorbing materials. That way, very little sound is re ected back from the barriers and little sound ampli cation occurs. A single absorptive barrier may also be more e ective than a single re ective one; sound which contacts the top of the barrier before reaching the other side would be absorbed, causing noise levels behind the barrier to decrease. Constructing barriers out of sound absorbing materials is more expensive, and so researching the e ec- tiveness and the optimal placement of absorption is important. The increase in barrier height equivalent to adding sound absorbing material is a convenient way to quantify the bene t of these barriers. The use of sound absorptive barriers is one factor a ecting barrier performance that was investigated here. Many barriers are located near trees or other foliage, and the e ect this has on the performance of barriers is unclear. One e ect could be that the foliage back-scatters sound which would normally reach the shadow zone | the area shielded from sound by the barrier | back towards the road, decreasing noise levels behind the barrier. Another possible e ect is that sound is absorbed by the foliage, causing energy to be converted from sound into vibrations of the leaves and branches. This would also lead to a decreased sound level behind the barrier, e ectively improving the performance of the barrier. The third possible e ect is that the foliage scatters sound into the shadow zone which would normally pass above the barrier, increasing the sound level behind the barrier and e ectively decreasing the barrier’s performance. Studying the e ects of foliage on the performance of noise barriers is the second factor which was investigated here. 2Chapter 1. Introduction There are several investigative techniques available to test the e ectiveness of noise bar- riers: full-scale laboratory testing, scale-model testing,  eld-testing and prediction work. These will now be discussed in regards to the detailed objectives of this work. The objec- tives of this work were:  To determine the optimal amount and placement of absorption on a barrier and the e ects it has on barrier performance  To investigate the e ects of absorption on the performance of parallel barriers  To investigate the frequency-dependent e ects of di erent types of foliage on the performance of barriers  To determine the practical implications of this research The  rst objective was to determine the optimal amount and placement of absorption on a barrier and the e ects it has on barrier performance. To achieve this objective, a re ective wall was to be built on a hard  oor in an anechoic chamber. By absorbing all sound incident on the walls and ceiling by the use of  berglass wedges, the anechoic chamber creates ideal outdoor conditions. Absorptive materials were to be added to the wall in di erent con gurations to determine the optimal amount and placement with regard to the barrier’s e ectiveness. Another method to be used to achieve this objective was to use computer modelling. Three di erent prediction models implemented in MATLAB were to be used to predict the results of the full scale anechoic chamber measurements: ray tracing,  nite elements and the method of images. This was to be done to validate the models, in hopes of using them to predict conditions similar to those found in the  eld. The second objective was to investigate the e ects of absorption on parallel barriers. It was desired to know if adding absorption reduced or removed the ampli cation which was seen for parallel re ective barriers. A scale model was to be created in the anechoic chamber 3Chapter 1. Introduction to achieve this objective. Scale-model materials were to  rst be selected, as material properties are not constant with frequency and play a crucial role in the e ectiveness of a noise barrier. A four-lane highway con guration was to be created, where one or two barriers, either re ective or absorptive, could be set up and tested. If the prediction methods stated above proved to be valid, predictions of re ective and absorptive parallel barriers were to be performed. The third objective was to investigate the frequency-dependent e ects of foliage on the performance of noise barriers. One method used to achieve this objective was to perform  eld tests along highways. Each site was required to have foliage in some con guration near a barrier and to be located near a stretch of barrier with no foliage. Frequency-dependent sound levels from the passing tra c were to be measured simultaneously behind the foliage and no-foliage sections of the barrier, and the results compared. This way, the e ects of the foliage could be isolated from other factors, such as barrier con guration and tra c noise variability. The scale-model created for the testing of absorption was to be used here to test the e ects of foliage growing near a barrier. Scale-model foliage was to be chosen which accu- rately modelled full-scale foliage. This foliage was then to be placed in di erent con gura- tions around barriers similar to those seen in the  eld. Sound levels were to be measured with and without the foliage. Computer modelling was also to be used to achieve this objective. Ray tracing was to be used to predict measurements performed on tree foliage to determine how the foliage should be modelled. Once this was accomplished, this program was to be used to further predict the e ects of foliage on the performance of barriers. The  nal objective of this research was to determine how the  ndings could be applied in the  eld. Once the above testing was completed, the practical implications were to be stated and recommendations given. 4Chapter 1. Introduction This work is organized as follows. Chapter 2 discusses acoustic theory which is relevant to this work: the wave equation, surface acoustical properties, outdoor sound propagation and noise barriers. Chapter 3 reviews the literature on absorptive noise barriers, sound propagation through foliage and the e ect of foliage on noise barriers. The detailed ob- jectives of this work are then discussed. Chapter 4 describes the full-scale experiment performed in the anechoic chamber and discusses the results. Chapter 5 discusses the  eld tests performed at several test sites with di erent foliage con gurations near barri- ers. Chapter 6 describes the theory behind scale modelling, as well as previous work done with scale models to study noise barriers. It then describes the scale-model experiment, model material selection and scale-model results. Chapter 7 discusses the three prediction methods and two di raction algorithms used to predict the results of several measurements done previously in the thesis. The predictions done here are discussed and the results are compared with measurements. Chapter 8 presents the conclusions of the completed work as well as discusses possible future work. 5Chapter 2 Theoretical Considerations 2.1 The Wave Equation Sound propagates as waves, and therefore the governing equation in acoustics is the wave equation: r2p 1 c2 @2p @t2 = 0; (2.1) where r2 = @ 2 @x2 + @2 @y2 + @2 @z2 is the three-dimensional Laplacian operator using Cartesian coordinates, p is the acoustical pressure in Pa, and c is the temperature-dependent speed of sound in m/s: c = 20 p T + 273:15; (2.2) where T is the temperature in oC. The speed of sound is also related to the frequency f in s 1 and wavelength  in m of the wave, by c =  f . Using separation of variables and assuming a harmonic time dependence ei!t, where ! is the angular frequency equal to 2 f , Equation 2.1 can be rewritten as the Helmholtz Equation: r2p+ k2p = 0; (2.3) where p is the time-independent pressure and k = !c = 2  is the wavenumber in m  1. In free- eld conditions, the radiative boundary condition is implemented, which enforces 62.2. The Decibel the sound pressure to go to zero as it travels an in nite distance from the source: lim r!1 p(r) = 0; (2.4) where r is the distance from a point source, using spherical coordinates. A solution to the Helmholtz equation using this boundary condition is: p = ps e ikr r ; (2.5) where ps is the source amplitude. 2.2 The Decibel When discussing sound levels in Pascals, the range of values is very large. Therefore, noise levels are typically converted from Pascals (Pa) to a logarithmic scale called decibels (dB). There are several de nitions of the decibel. One relates to the sound pressure level, which is de ned to be zero at a reference level p0 = 2x10 5 Pa. This is considered to be the minimum audible sound pressure for the average person. The sound pressure level Lp in dB is de ned in terms of the pressure p in Pa as: Lp = 20 log10  p p0  : (2.6) The sound power level is another decibel which is commonly used, de ned with reference to W0 = 10 12 W. Because sound power is proportional to p2, it can be calculated in a similar way to Lp, however with a factor of 10 in front instead of 20: Lw = 10 log10  W W0  : (2.7) 72.3. Surface Properties 2.3 Surface Properties There are three ways a sound wave can react when it hits a surface; it can be re ected, absorbed and transmitted. The amount of each that occurs is dependent on the material, the frequency and the angle of incidence. The amount of sound energy re ected from a surface is determined by the complex re ection coe cient  , which is de ned as the ratio of the re ected energy to the total incident energy. Sound can be re ected in two ways: specularly or di usely. In specular re ection, the angle of incidence equals the angle of re ection. When di use re ections occur, sound is re ected in all directions. Sound can also be transmitted through the material. The transmission coe cient  is de ned as the ratio of the energy transmitted to the incident energy. Energy that is neither re ected nor transmitted is absorbed by the material, with an absorption coe cient  . Conservation of energy states that:  +  +  = 1: (2.8) In many cases, a complex pressure re ection coe cient R is of interest, as a surface can change the phase of a wave, which is not accounted for when using an energy-based coe cient. One can derive the energy coe cient  from R by:  = jRj2; (2.9) as energy is proportional to the pressure squared. Assuming that transmission through a material is negligible (  0), as assumed here for many surfaces such as noise barriers, and for in nitely thick materials such as grounds, the absorption coe cient  can be derived from R as:  = 1 jRj2: (2.10) 82.4. Outdoor Sound Propagation Surfaces can be quanti ed either by their re ection and absorption coe cients or their acoustical impedance Z, measured in Rayls (Pa s/m). The speci c acoustic impedance of a material is de ned as: Z = p u ; (2.11) where p is the acoustical pressure and u is the particle velocity. The characteristic impedance of a medium is given as: Z =  c; (2.12) where  is the density of the medium in kg/m3 and c is the speed of sound in that medium. Ground surfaces can be characterized as either locally or extended reacting. They are locally reacting when the speed of sound in the ground is much lower than the speed of sound in air. This causes the sound in the ground to propagate normal to the ground surface, regardless of the sound’s angle of incidence on the ground. Therefore the ground impedance is independent of the angle of incidence. When this is not the case, extended reaction occurs and the impedance is dependent on the angle of incidence. 2.4 Outdoor Sound Propagation Outdoor sound propagation in the simplest case involves a source and a receiver above a specularly-re ecting plane. There are two sound paths between the source and receiver, as shown in Figure 2.1: the direct path and the re ected path. The sound pressure at the receiver is therefore given by: p = ps  e ikrd rd +R e ikrr rr  ; (2.13) where ps is the source amplitude, R is the re ection coe cient of the ground, and rd and rr are the direct and re ection sound path distances, respectively. 92.4. Outdoor Sound Propagation Figure 2.1: Idealized sound propagation between a source S and receiver R over a ground surface. Sound propagating in a free  eld is attenuated due to geometrical spreading: 3 dB per doubling of distance for cylindrical waves and 6 dB for spherical waves. The re ected sound path is longer, and therefore is subject to more attenuation due to geometrical spreading. The sound is also attenuated due to the re ection from the ground if the magnitude of the re ection coe cient is less than one. A phase change during re ection can also occur. Because of this path length di erence, constructive and destructive interference occurs between the direct and re ected waves. Because of this interference, dips in the sound level will occur at several frequencies. In the case of acoustically hard ground, these frequencies correspond to when the path length di erence is an odd multiple of  =2, where the waves are 180o out of phase. Several atmospherical e ects occur which impact the propagation of sound outdoors. Absorption by air occurs, causing the sound pressure of a wave to decrease as it propagates through air. Energy is converted into modes of vibration of oxygen and nitrogen molecules, and is dependent on frequency, relative humidity and temperature. These e ects only become signi cant at high frequencies or large distances. Other atmospherical e ects include wind and temperature gradients [2] and turbu- lence [3]. Wind and temperature gradients a ect the speed of sound, causing it to vary 102.5. Noise Barriers with height; therefore sound waves refract in the atmosphere. As these phenomena a ect the performance of noise barriers only for large propagation distances, they are not relevant in this work. Turbulence consists of random eddies in the air, which can change the local direction or amplitude of sound waves at random and may a ect the performance of a noise barrier in an unpredictable way. Because of this, prediction models which do not take turbulence into account may vary from measurements. 2.5 Noise Barriers The e ectiveness of a noise barrier is quanti ed by the insertion loss (IL), the change in sound level at a certain receiver position due to the barrier, given as: IL = Lp;nobarrier  Lp;barrier (2.14) where Lp;nobarrier and Lp;barrier are the sound pressure levels taken without and with the barrier, respectively. A positive IL indicates a reduction in noise levels, while a negative IL indicates an increase (ampli cation). Sound reaches the opposite side of a noise barrier by means of di raction, the bending of sound waves around an edge. The amount of sound that is di racted depends on the thickness and absorption of the edge, as well as the source and receiver positions and frequency. There are several models used to predict di raction, which are discussed in Section 7.1. Typically, the IL of a barrier increases with frequency, meaning that less sound is di racted as the wavelength decreases. Maekawa [4] developed a simple method of predicting the IL of a semi-in nite plane 112.5. Noise Barriers Figure 2.2: Typical A-weighted tra c-noise spectrum used to determine total A-weighted IL’s. [5] screen in a free- eld. He de ned a Fresnel number N to be: N =  2  (2.15) where  is the path length di erence between a direct source-receiver path and a source- edge-receiver path. The negative sign is used when there is a direct line of sight between the source and receiver. From N , one can determine the IL from a graph, which shows the IL increasing monotonically with N and therefore frequency. When studying roadside noise barriers, the sound source of interest is tra c, which has a characteristic frequency spectrum. Figure 2.2 shows a typical A-weighted tra c spectrum, measured by Wake eld Acoustics [5]. A-weighting takes human hearing into account, as people do not perceive every frequency to be of equal loudness. As well as considering the frequency-dependent IL, it is of interest to consider the total IL, where Lp;nobarrier and Lp;barrier are the total levels which encompass all frequencies. 122.5. Noise Barriers When discussing the total IL, it can be given in A-weighted decibels (dBA) so as to relate to what people would hear. The results in this work that are presented as A-weighted IL’s have been calculated using the A-weighted tra c noise spectrum in Figure 2.2 as a reference. When a sound source was used, its power output was subtracted from the noise levels and then the A-weighted tra c spectrum was added, before summing the levels up over all frequencies to get a total value. These totals in dBA were then subtracted as in Equation 2.14 to determine the total A-weighted IL. As a reference of acceptable IL values, the B.C. Ministry of Transportation and Infrastructure Noise Policy [1] states that a mitigating noise wall must provide an IL of at least 5 dBA. 13Chapter 3 Literature Review and Objectives This chapter reviews existing literature on the e ects of using absorptive noise barriers. It then discusses the literature on sound propagation through foliage, followed by the e ects of combining foliage with noise barriers. Once this literature is reviewed, the detailed objectives of this work are presented. 3.1 Absorptive Noise Barriers Rawlins [6] conducted theoretical studies on the di raction of sound by an absorbent edge of a screen. He solved the boundary value problem of a rigid barrier with an absorbent edge, which he then studied asymptotically. He showed that a strip, one wavelength wide, of absorbent material at the top of a half plane led to the same di racted sound  eld as a fully covered screen. Fujiwara et al. [7] derived approximate theory for di raction around an absorptive barrier. They then developed charts which had the e ects of absorption in dB as a function of the re ection coe cient of the absorptive surface. Di erent charts were made for various angles of di raction. They found large absorption e ects of up to 7 dB. Isei [8] developed a prediction method which used the speci c  ow resistance to de ne the acoustical properties of a barrier and ground. He saw that the  eld behind a barrier showed interference between the direct and re ected sound paths. He found that the type of ground in uenced the IL more than the absorption of the barrier. May and Osman [9] used a 1:16 scale model to study di erent shapes of noise barriers. 143.1. Absorptive Noise Barriers They tested both absorptive and re ective noise barriers and found that making the source side absorptive resulted in a measurable reduction in the ampli cation due to parallel barriers. They found that the higher the NRC value of the absorptive material, the greater the improvement of the IL. For a single barrier, using a point source, covering the source side of a thin barrier with absorptive material gave an IL increase of 0.8 dBA. Covering the top of a 2.44 m wide barrier with absorptive material gave an IL increase of 2 dBA over a wide re ective barrier. They studied the 500 and 1000 Hz third-octave bands, but did not perform a more detailed frequency analysis. Bowlby et al. [10] used geometrical acoustics to study re ections from a re ective noise barrier and the e ects it had on the performance of parallel noise barriers. They found that using sound absorptive material on parallel barriers minimized the increase in noise caused by these re ections. Tobutt and Nelson [11] used a computer model to test the e ectiveness of absorptive treatment on 3 m high parallel noise barriers set 45 m apart. The receivers were set 20 to 70 m behind the barrier and up to a height of 4.5 m. The di erence in noise levels with and without absorptive treatment ranged from 1.5 to 3 dBA. Fujiwara, Hothersall and Kim [12] used a boundary element model to study the insertion loss of noise barriers with rectangular, T-shaped and cylindrical edges and rigid, absorbing or soft surfaces. They found the mean IL for the rectangular, absorbing barrier to be 3.9 dB higher than for the rectangular and rigid barrier. They found that cylindrical edges and soft surfaces made for the most e ective barrier. Morgan, Hothersall and Chandler-Wilde [13] also used a numerical boundary element model, this time examining track-side railway noise barriers. They studied di erent shapes of barriers, both with re ective and absorbing surfaces. The results from the two models were compared. Two source distances were considered, corresponding to both the near and far sides of the tracks | approximately 3 and 8 m away, respectively. They found 153.1. Absorptive Noise Barriers that adding an absorbing surface to the track-facing side of a barrier signi cantly improved the performance. When the source was on the near side of the track the IL increased by approximately 10 dB when an absorptive surface was added. When the source was on the far side of the track the IL increased by approximately 4 dB. Increasing the height of the absorbing barrier also improved the performance. Watts and Godfrey [14] studied the e ects on roadside noise levels of applying sound- absorptive materials to the tra c face of noise barriers. They chose two sites. The  rst site had a single 3 m high barrier erected next to an eight-lane highway. The other site had 3.7 m high barriers on both sides of the road which ran in a shallow cutting, with a separation distance of 34 m. Both sites had the same absorbent panels on the tra c side and were re ective on the reverse side. They measured both sites as they were, and then reversed the panels such that the re ective side faced the tra c. For the 3 m high barrier, which was placed 5.6 m from the edge of the road, receivers were placed 9.5 m behind the barrier, at heights of 1.7, 2.7 and 4.7 m. For the other site, where the barrier was 7.5 m from the road, receivers were placed both 15 and 30 m behind the barrier; they were at heights of 1.5, 4.5 and 7.5 m. In both cases they placed a reference microphone further down the road where there were no barriers set up. They found, in both cases, that there was a decrease in noise due to absorption of generally less than 1 dB when the absorptive side faced the tra c. The one exception was in the second case, where the receiver was 15 m behind the barrier and at a height of 7.5 m. Here there was a decrease in noise of around 2 dB. In general, the results were lower than predicted. Previous studies have been done in anechoic chambers at full scale to study absorption. L’Esperance, Nicolas and Daigle [15] built a barrier in a semi-anechoic chamber. The barrier had a height of 0.577 m and was 5 m in length. The barrier was made of 2.5 cm thick plywood, with the upper 1.0 cm tapered to a sharp edge. A source was placed 0.6 m from the barrier, at a height of 1.1 cm. The receiver was placed at 1.2, 0.6, 0.3 and 0.15 163.1. Absorptive Noise Barriers m from the barrier on the receiver side in four di erent tests, all at a height of 6 mm. They measured the insertion loss for three barrier conditions: both sides of the barrier re ective, the source side of the barrier covered with a 4 cm thick  berglass layer, and both sides covered with the  berglass. They compared these results to theory, which combined an approximate di raction solution with a classical theory for propagation over ground. The experiment examined the e ect of the angle of di raction on the insertion loss. The results showed that the e ect of the absorptive layer can increase the IL by up to 10 dB when the di raction angles are large. They examined two previous studies on barrier absorption which gave contradicting results. They pointed out that when the results in Isei’s work [8] showed little increase in IL due to absorption, the angle of di raction was quite low (source and receiver 2 m away from a barrier 0.26 m high). They found that when a greater increase in IL was seen in Fujiwara’s work [7], the di raction angles were greater. They found that covering both sides with an absorbent barrier increased the IL, espe- cially when both the receiver and the source were located near the barrier. The results also showed that covering the receiver side was just as e ective as having the source side covered. They saw an IL increase of 2 dB when the absorptive layer was added to the source side, and a greater increase (ranging from 1-7 dB, depending on the angle) when both sides were covered. Ilgurel and Sozen [16] built a wall in a semi-anechoic chamber with dimensions 11 m x 6 m x 4.5 m. The barrier was 2.6 m high, made from two-sided 12 mm gypsum panels with a 10 cm air gap and a 5 cm Rock-wool  lling. Measurements were taken with and without a 5 cm thick Rock-wool layer on one entire side of the barrier (the side facing the source) as an absorptive layer. The noise source was placed 1 m high and 1 m away from the barrier. Receivers were placed on seven di erent axes, 15 degrees apart, ranging from 0 degrees (directly above 173.2. Tree Foliage the barrier) to 90 degrees (perpendicular to the barrier). Six receivers were placed on each axis, 1 m apart. The lowest receiver was placed at a height of 1.6 m. Results were obtained for overall and 125-8000 Hz octave-band levels. They found noise reduction levels between 13.3 and 15.4 dBA without the absorptive layer and between 16.3 and 20.0 dBA with the absorptive layer. Speci cally, they found possible noise reductions due to the absorptive layer of 1.5-3.5 dBA. This was not found for the receivers set up at 0-30 degrees, where there was still a direct line of sight from the source to the receiver. The absorptive layer provided extra noise reduction at frequencies over 1000 Hz. 3.2 Tree Foliage 3.2.1 Sound Propagation Through Foliage The  rst study of the e ects of foliage on sound was in 1946, performed by Eyring [17]. He investigated the sound propagation through a jungle during the wet season in Panama. He measured sound produced by loudspeakers over several hundred feet. He concluded that within a jungle, temperature and wind gradient e ects are negligible. Terrain loss coe cients, ignoring spherical divergence, were found to increase with frequency and have total values of 0.05-0.13 dB/m. Typical loss coe cients over open terrain were found to be 0.003-0.03 dB/m, depending on the thickness of the grass. Wiener and Keast [18] measured the excess attenuation of sound through a dense evergreen forest, where trees were 6-12 m tall. They also found that attenuation increased with frequency, with approximately attenuation coe cients of 0.03 dB/m at 500 Hz and 0.20 dB/m at 4000 Hz. Another trend reported in literature was higher foliage attenuation at low and high frequencies with a decrease at middle frequencies [19] [20] [21]. Attenuation coe cients of 0.2 to 0.6 dB/m were seen. Morton [21] noted that as he measured further from the ground, the low frequency attenuation decreased and the trend became similar to that 183.2. Tree Foliage seen by Eyring, an increase in attenuation with frequency; he found values going from 0.10 dB/m at 100 Hz up to 0.30 dB/m at 10 kHz. Therefore, the low frequency attenuation was attributed to ground e ects; grounds beneath trees contain roots, which a ect the porosity and impedance. Cook and Van Haverbeke [22] looked into using trees and shrubs for noise abatement in great detail. They studied many di erent types and con gurations of trees with three di erent noise sources: a diesel truck, an urban bus and arterial cars. For a 6 m thick tree belt with shrubs to increase density, they found an attenuation of 8 dBA when taken 6 m behind the foliage. They also found that putting the trees closer to the source rather than the receiver increased the attenuation provided by the foliage. They recommended, for moderate-speed cars in urban areas, to use 6 to 15 m wide belts of trees and shrubs, with the trees placed as close to the road as possible. Measuring the attenuation provided by tree belts was done by Kragh [23], who measured sound levels from passing trains, both over a grass terrain and through tree belts. The author stated that the attenuation found by taking the di erence of the two measurements was both due to the foliage and variations in terrain, whose e ects were impossible to separate. It was found that a dense, 50 m wide tree belt which contained beeches, birches, elms and various conifers provided 8 or 9 dB of attenuation. A dense, 25 m wide belt which consisted of oaks, hornbeams, poplars, silver  rs and various bushes was found to give 6 or 7 dB of attenuation. Several studies were done on both foliated and defoliated trees to determine the e ects of the foliage compared to the branches. Aylor [20] examined the same hardwood brush in summer and in autumn. He found a decrease in attenuation of up to 0.16 dB/m in the autumn. He found increasing leaf density reduced sound transmission. Aylor also studied the e ect of leaf size and density on the sound transmission of trees [24]. He found that to attenuate noise e ectively, vegetation should be dense and broad-leafed. 193.2. Tree Foliage Price et al. [25] measured sound propagation through trees during the winter and the summer to determine the e ects of trees with and without foliage. They found signi cant di erences between winter and summer, both in a peak attributed to ground e ects and in the high-frequency attenuation, which increased by up to 10 dB in the summer. They then developed prediction models which included contributions from the ground e ects and the dimensions and density of both the trunk and other foliage. Martens [26] set up foliage testing in an anechoic chamber using di erent plants in earthenware pots. He measured the sound pressure level 6 m from the source for several foliage situations: pots with no foliage, birch trees fully defoliated with stems and branches present, half of the 46 trees foliated, and then all of them foliated. There was little di erence found between the  rst two cases up to 8000 Hz. At 8-10 kHz, where the wavelength corresponded to the dimensions of the birch tree stems, a 3 dB drop in sound pressure level was seen. When looking at the in uence of foliage, a general trend was seen. Some noise ampli cation was measured at mid-frequencies up to a certain frequency, depending on the type of plant, above which a drop in noise was seen. An empirical formula was developed by Hoover [27], who performed many measure- ments of sound propagating through a forest. He gave the attenuation due to foliage Af in dB as: Af = 0:01rff 1 3 : (3.1) Here, rf is the distance in meters and f is the frequency in Hz. 3.2.2 Foliage and Barriers While much work has been done on studying sound propagation through foliage, there have been only a few studies on the e ects of the performance of barriers placed near foliage. Cook and Van Haverbeke [28] studied the combination of barriers with trees as a method of noise control. They compared the total A-weighted sound levels behind di erent con- 203.2. Tree Foliage  gurations, including bare walls, trees and walls with trees, with no walls or foliage. They found that trees gave approximately 4-5 dBA of attenuation, while a bare wall gave 10-11 dBA and trees with a wall gave 13-14 dBA of attenuation. Renterghem et al. [29] studied the e ect of using tree foliage as a wind screen to prevent the refraction of sound around a barrier in a downwind direction. Sound refraction occurs when the speed of sound changes with height, as occurs in wind. The bending of sound waves can make a barrier less e ective at large distances and therefore preventing this e ect is desirable. They created a 1:20 scale model in a wind tunnel and used windscreens to model the scale-model trees. They  rst con rmed the decrease in IL when wind was present,  nding IL decreases of up to 8 dB at a distance of 10 times the barrier height away from the barrier. Once the windscreens were inserted, in the absence of wind they found that the change in IL was very small and sometimes negative. They attributed this to the scattering of the wind screen. For farther distances when wind was present, the windscreen always increased the IL, by up to 4 dB. When closer than  ve times the height of the barrier, no e ect was greater than 1 dB. Renterghem et al. [30] also performed  eld tests, where measurements behind a noise barrier with and without trees were compared. They found that for downwind sound propagation, the trees increased the e ectiveness of the noise barrier. As wind speed increased, so did the improvement in performance by the barrier; improvements of up to 4 dBA were seen for winds at 12 m/s. For upwind sound propagation, trees only a ected the performance slightly, starting with a slightly negative change in IL for low velocity winds and increasing to 0.5 dB for faster-moving winds. They did a frequency dependent study on noise levels behind a barrier with and without a single row of 8 m tall trees behind it in the absence of wind. They found that at low frequencies, noise levels in the no-trees case were higher; above 1000 Hz they found that noise levels in the treed case were higher, with all e ects under 5 dB. 21Chapter 4 Full-Scale Laboratory Testing In the research described in this chapter, a full-scale re ective barrier was built in an anechoic chamber to better understand the e ects of absorption placement on a single bar- rier’s performance. This was achieved by placing three di erent absorptive materials on the re ective wall in di erent con gurations. These materials had their absorption coe - cients measured by two techniques: the spherical decoupling method and the impedance tube method. Insertion loss measurements were  rst made using a porous absorber as the surface absorption. Then measurements were made using two commercially available absorbent barrier treatments. The insertion loss was measured in third-octave bands for various con gurations of the re ective and absorptive barriers; from these, total A-weighted values relevant to a typical tra c-noise spectrum were calculated. Soft ground e ects, oc- curring when the barrier is placed on an acoustically soft surface, were also examined. The size of the anechoic chamber limited the source and receiver distances and the height of the wall, and therefore realistic dimensions could not be achieved. 4.1 Absorption Measurements Two methods were used to determine the normal-incidence absorption coe cients of the ab- sorptive surfaces: the spherical decoupling method [31] and the impedance tube method [32]. 224.1. Absorption Measurements Figure 4.1: The spherical decoupling method geometry [31]. 4.1.1 Spherical Decoupling Method The spherical decoupling method uses two microphones located perpendicular to a material at some spacing to determine its acoustical properties. The transfer function between the microphones is measured and from this the complex sound re ection coe cient, energy absorption coe cient and acoustical impedance can be calculated. Figure 4.1 shows the set up of a typical measurement. Two microphones, M1 and M2 are placed at heights h1 and h2 above a surface. A source S is placed at height H above the surface, creating an angle of incidence  with the surface beneath the microphones. Assuming specular re ection and a time dependence of ei!t, the pressure at each mi- crophone is given as: Pj(f;  j) = Po(f)  e ikr1j r1j +R (f;  j) e ikr2j r2j  ; (4.1) for j = 1; 2, where Po(f) is the source amplitude and R(f;  ) is the re ection coe cient [31]. The frequency response function between microphones, de ned as H12 = P2(f; ) P1(f; ) , can be 234.1. Absorption Measurements simpli ed to: H12(f;  1;  2) = e ikr12 r12 +R (f;  2) e  ikr22 r22 e ikr11 r11 +R (f;  1) e  ikr21 r21 : (4.2) For su ciently large source heights and small receiver heights,  1   2   . By using this approximation and rearranging Equation 4.2, the complex re ection coe cient is given by: R(f;  ) = e ikr12 r12  H12(f;  ) e  ikr11 r11 e ikr21 r21 H12(f;  ) e  ikr22 r22 : (4.3) The energy absorption coe cient  can be derived from the re ection coe cient by the following equation:  = 1 jRj2; (4.4) which assumes that no sound is transmitted through the material. The impedance, as a function of the re ection coe cient, is given as: Z = 1 +R(f;  ) 1 R(f;  ) 1 cos   1 + 1ikro  ; (4.5) where ro is the distance from the source to the ground directly beneath the microphones. This method is not valid at all frequencies. Boden and Abom [33] examined ways to minimize the error in the re ection coe cient when using the two-microphone method. They suggested the following frequency limits: 0:1  c 2(h1  h2) cos  < f < 0:8  c 2(h1  h2) cos  : (4.6) 4.1.2 Impedance Tube Method The impedance tube method is also a two-microphone method, although the measurements only apply to normal incidence. The impedance tube is a hollow tube which has a loud- speaker at one end and the material of interest placed at the other; the size of the tube 244.2. Experimental Setup varies depending on the frequency range of interest. The sample of the material must be a circle with a diameter matching that of the tube, in this case 10 cm. Two microphones are inserted into the side of the tube so they are set up perpendicular to the sample and the loudspeaker. The equations from the previous section still hold, although now  = 0 and therefore cos  = 1. The re ection coe cient can therefore be written as: R = H12  e iks eiks  H12 eikh1 ; (4.7) where s is the spacing between the microphones. The impedance is calculated from the re ection coe cient by: Z = 1 +R 1 R : (4.8) The impedance tube is limited to frequencies below which only plane waves propagate in the tube and at which wavelengths are greater than twice the microphone spacing, causing the upper limit to be given by the minimum of the following [32]: fu < 0:58 c d (4.9) fu < 0:45 c s ; (4.10) where d is the tube diameter and s is the spacing between the microphones. The lower frequency limit is [32]: fl > 0:05 c s : (4.11) 254.2. Experimental Setup Figure 4.2: The re ective barrier in the anechoic chamber. 4.2 Experimental Setup The tests were done in an anechoic chamber with dimensions 4.1 m x 4.7 m x 2.6 m. A 3.66 m x 3.66 m  oor was built on top of the existing wire mesh  oor, as a strong support and re ective surface for the wall to be placed on. This allowed for outdoor conditions to be modelled, with perfectly absorbing walls and ceiling and a sound re ective ground. The  oor was made of seven 3.66 m long 2x4’s, evenly spaced on the wire mesh  oor, with 19 mm plywood boards screwed on top. The wall, shown in Figure 4.2, was 3.66 m long and 1.22 m high, and was made from 12 mm drywall on either side of a wooden frame, made from 2x4’s. An extra layer of 12 mm drywall was screwed onto the source side of the wall to increase the transmission loss. To reduce sound transmission, the cavity was  lled with  berglass batt insulation. Air gaps between the barrier and the  oor were  lled with putty. The wall was set up in the center of the  oor in the chamber. Absorptive materials were hung in di erent con gurations on the faces of the wall, including either half or all of either the source and receiver sides. Due to lack of absorbent materials, all of both sides were not simultaneously covered. 264.2. Experimental Setup Figure 4.3: The barrier con guration, including source and receiver positions. Note that R6, R7 and R8 correspond to the same di raction angle. The sound source was placed 1 m behind the barrier, at heights of 0.25 and 1.0 m. The sound sources used were omni-directional point sources | one for high frequency (above 500 Hz) and the other for low frequency (below 500 Hz) [34]. Figure 4.3 shows the test con guration. The receiver was placed at distances of 0.6, 1.2 and 1.8 m on the non-source side of the barrier, at heights of 0.2 and 1.05 m. The receiver was also placed 1.8 m behind the barrier at a height of 0.75 m, and 1.2 m behind the barrier at a height of 0.9 m. This allowed for examination of both di erent angles of di raction as well as varying distances at a constant angle. Receiver positions were also on the source side for the low source height, 1.8 m away, at heights of 0.75 and 1.05 m in order to measure the e ects of re ections from the barrier. A Bruel & Kjaer 1/2" type 4190 microphone was used, along with a B&K type 2669 preamp. A SINUS Soundbook was used as the white-noise signal generator and the analyzer, allowing both narrow-band and limited-band analysis. 274.3. Absorptive Materials (a) (b) Figure 4.4: The commercial absorbent materials on the barrier: a) Durisol; b) Whisper- Wall. 4.3 Absorptive Materials The  rst absorptive material used on the wall was cotton acoustic ba es. Each ba e was 1.22 m x 0.61 m and 25 mm thick. Two layers of these ba es were used, giving a total thickness of 50 mm. Two di erent commercial absorbent barrier surfaces were also tested. The  rst involved Durisol panels which were each 1.22 m x 0.61 m and made of cement and wood  bers. One side of the panels was  uted, with a base of 5.1 cm and a  ute depth of 3.2 cm. Figure 4.4(a) shows the Durisol panels covering one side of the barrier. The other commercial absorbent barrier surface tested was WhisperWall. The tiles were 0.61 m x 0.61 m and were 10.2 cm thick. Figure 4.4(b) shows the WhisperWall tiles covering one side of the barrier. The normal-incidence absorption coe cients of these materials were measured using the spherical decoupling method and the impedance tube method. The frequency range of validity for the set up used here for the spherical decoupling method was 340 to 2750 Hz and for the impedance tube was 250 to 2000 Hz. The random-incidence absorption coe cients ( RI) of the three absorbent materials were calculated on the assumption of 284.3. Absorptive Materials (a) (b) Figure 4.5: Random-incidence absorption coe cient as measured by: a) the spherical decoupling method; b) the impedance tube method. local reaction by the following equation:  RI = 8  1 +   2   2   tan 1    2 +  ( + 1)    ln  ( + 1)2 +  2  2 +  2   ; (4.12) where  = Re  1 Z  ;  = Im  1 Z  : (4.13) These values are shown in Figure 4.5. 294.4. Results Figure 4.6: Half of the re ective wall covered in the acoustic ba es. Using the impedance tube results, the NRC values | the average octave-band absorp- tion coe cients at 250, 500, 1000 and 2000 Hz | were calculated. The NRC of the ba es was 0.71, of the Durisol panels was 0.56, and of the WhisperWall tiles was 0.64. Note that there is some reason to believe these WhisperWall panels had not been manufactured in a way to optimize their sound absorption. 4.4 Results 4.4.1 Acoustic Ba es The ba es were attached to the wall using insulation hangers; they were attached in  ve di erent con gurations, which covered the barrier as follows: the full source side, the top half of the source side, the full receiver side, the top half of the receiver side, and the top half of both the source and receiver sides. Figure 4.6 shows the top half of the source side of the wall covered with ba es. The insertion losses of these con gurations and of the re ective wall were measured. 304.4. Results (a) (b) Figure 4.7: Measured third-octave insertion loss at receiver position R6 for di erent ba e con gurations for: a) the low source position; b) the high source position. The IL in third-octave bands at receiver position R6 is shown in Figure 4.7 for the di erent ba e con gurations. For the low source position, the absorptive material was more e ective at increasing the IL in the frequency ranges where the ba es were highly absorptive. Between 300 and 400 Hz, where the absorption coe cient of the ba es was highest, covering the top half of both sides increased the IL by 7-8 dB over that of the re ective wall, a 4 dB increase over any other absorptive con guration. At frequencies above 1000 Hz, where porous absorbers were expected to be highly absorptive, there was 314.4. Results Figure 4.8: The A-weighted insertion loss for the low source position as measured at the source-side receiver positions, for various con gurations of re ective and absorptive barriers. a 3-5 dB increase in IL due to covering the top half of both sides with ba es. For the high source position this high frequency increase in IL was again seen; however below 1000 Hz there was very little increase in IL due to the absorptive treatment, regardless of the con guration. This was due to the smaller di raction angles that were present for the high source position. These trends were consistent for the other receiver positions. Figure 4.8 displays the total A-weighted IL at the source-side receiver positions for the low source height. The IL was expected to be negative since sound that, without the wall in place, would be absorbed by the chamber walls was now re ected back to the receiver. As expected, covering the full source side of the wall with absorptive material increased the IL to positive values, which con rmed it was highly e ective at preventing re ections. Figure 4.9 shows the total A-weighted insertion loss at each receiver position for both the low and high source positions for each ba e con guration. The re ective wall provided 12-18 dBA of attenuation, and the overall IL improvement due to absorption was 1-2 dBA. It was seen that, of the con gurations tested, placing the absorptive material on the top 324.4. Results (a) (b) Figure 4.9: Measured A-weighted insertion losses at the eight receiver positions on the non- source side of the barrier for di erent ba e con gurations for: a) the low source position; b) the high source position. The receiver positions are labeled 1 through 8 as shown in Figure 4.3. half of both sides of the wall produced the highest IL for both source positions, while the re ective wall produced the lowest IL, as expected. Covering the full side of the barrier compared to covering half | either the source or receiver side | showed an IL increase of approximately 0.5 dB. Covering the full side of both sides of the barrier was not tested; however based on the other measurements an improvement in IL of 2-3 dBA over the re ective wall could be expected. For the higher source position, R1, R2 and R3 showed the highest insertion loss. These 334.4. Results were the lowest receiver positions, corresponding to the greatest di raction angles and greatest path length di erences. Receiver R4 had the lowest IL, as it was the highest and farthest receiver position from the wall, giving it the lowest di raction angles and the smallest path length di erence. Receivers R6, R7 and R8 were positioned such that they had the same angle of di raction, and therefore the IL was expected to increase with path length di erence. Increasing IL’s from R6 to R8 was in fact seen in the results. For the lower source position, the IL at all receiver positions was higher compared to the higher source position, as expected due to the larger di raction angles. However the results were not as expected at several receiver positions. The IL decreased from R6 to R8, contrary to expectation. The IL at R3 was higher than at both R1 and R2, where it was expected to be lower. There may have been interactions between the direct and re ected waves, either constructive or destructive interference, which a ected the sound levels at particular frequencies for di erent receiver positions. 4.4.2 Commercial Absorbent Barriers The Durisol panels were screwed onto the re ective wall in three di erent con gurations: covering the full source side, the top half of the source side and the top half of both sides. In the  eld, the manufacturer constructs barriers with a solid concrete layer in the center and absorptive panels on either side. The WhisperWall tiles were measured in one con guration: covering the full source side of the barrier. This is the con guration that the manufacturer reported using in the  eld. The IL di erences between the three con gurations of the Durisol panels were very similar to those of the ba e con gurations. Covering the top half of both sides of the barrier gave the highest IL at receivers on the non-source side, and covering the full source side gave the highest IL on the source side of the barrier. The three di erent absorptive materials were compared for one con guration: covering 344.4. Results (a) (b) Figure 4.10: Measured A-weighted insertion losses for the re ective wall and for the full source side covered by the three absorptive materials for: a) the low source position; b) the high source position. The receiver positions are labeled 1 through 8 as seen in Figure 4.3. the full source side of the barrier. Figure 4.10 shows the total A-weighted IL of the re ective wall as well as of the full source side of the wall covered with the three absorptive surfaces. Based on the absorption coe cients, the ba es were expected to give the greatest IL since their absorption was the highest around 1000 Hz, where the tra c noise spectrum is at a maximum. This is what was seen in the results. Both Durisol and WhisperWall gave IL values 0.5-2 dB lower than the ba es. For the low source position, the Durisol and WhisperWall results were quite similar. For the high source position, the Durisol panels gave IL’s 0.5-1 dB higher than the WhisperWall tiles for almost all receiver positions. The 354.4. Results thickness of the WhisperWall tiles could cause this di erence. With the lower source posi- tion and higher di raction angles, the e ective thickness that sound had to travel through for the WhisperWall tiles was increased more than for the Durisol panels, which allowed for more opportunity for sound to be absorbed. At this e ective thickness, WhisperWall and Durisol were very similar. At the higher di raction angles, where Durisol out-performed WhisperWall, the e ective thickness was virtually the same as the actual thickness, and therefore the increase seen with the lower source position did not occur. This suggested that the Durisol panels absorbed more sound per distance than WhisperWall. 4.4.3 Soft Ground E ects When sound propagates over soft ground, a phase change occurs on re ection. Therefore destructive interference occurs between the direct and re ected waves. Typically in the absence of a barrier, acoustically soft ground creates a decrease in the noise level at low frequency. However when a barrier is inserted, this destructive interference does not occur, possibly resulting in increased noise levels and decreased IL. The acoustic ba es were placed on top of the plywood  oor, and the re ective wall and the wall with di erent con gurations of the Durisol panels were tested to see how the acoustically soft ground would a ect the IL. Figure 4.11 shows the results for the low and high source positions at receiver position R6. For the high source position, there was a dip in IL around 200 Hz for all absorptive con gurations. The IL became negative, meaning that the barrier did, in fact, increase noise levels. This dip was not seen for the low source position, however the large peak seen in Figure 4.7 was not present. The soft ground appears to have prevented the interference between the direct and re ected waves which occurred with the plywood  oor. Plywood can  ex and therefore absorb sound at low frequency. This can introduce phase changes and interference, causing the unsmooth nature shown in Figure 4.7 and not seen with the 364.5. Summary (a) (b) Figure 4.11: Measured third-octave insertion loss at receiver position R6 for di erent Durisol con gurations, with acoustic ba es covering the re ective  oor creating a soft ground, for: a) the low source position; b) the high source position. soft ground. The absorptive material on the wall had similar e ects on the IL as for the hard ground case. 4.5 Summary Di erent con gurations of absorbent material on a 1.2 m high re ective stud wall in an anechoic chamber were examined. Receivers were placed 0.2-1.05 m high and 0.6-1.8 m from the barrier, while the source was placed 1 m from the wall, either 0.25 or 1 m high. It was 374.5. Summary found that of the con gurations tested the highest IL for non-source side receiver positions came from covering the top half of both sides of the barrier with absorbing material, improving the IL by 1-2 dBA. Covering the full source side with absorbing material gave the highest IL on the source side of the barrier, preventing the sound ampli cation seen with a re ective wall from occurring. The bene t of this to the non-source side of parallel barriers could not be con rmed with just one wall, but further testing with scale models was done to investigate this. Materials with the highest absorption coe cient | in this case the cotton acoustic ba es | gave the greatest increase in the IL; the performance of two commercial absorbent barrier surfaces was slightly lower. The e ects of absorptive surfaces on the IL were similar for both hard and soft ground. 38Chapter 5 Field Tests Field tests were performed at several locations along highways to better understand the e ects of nearby foliage on noise barriers. Sites were chosen which had some con guration of foliage near a barrier, as well as a long stretch of bare wall to use as a reference. Noise levels behind both sections of the barrier were simultaneously measured, so that the e ects of the foliage could be isolated. The  rst site was on 59A St. along Highway 17 in Ladner, British Columbia. Then data were collected on Vancouver Island at three sites: along Nanaimo Parkway near the intersection with Highway 1, on Highway 1 near Helmcken Road, and on Highway 17 near McKenzie Avenue. The equipment used was the Rion NA-28 SLM, the Sinus Soundbook and the Larson-Davis SLM. The microphones were nominally set up 6 m from the barrier, and 1.5 m below the tops of the barriers, which were typically 3 m tall. Each microphone was calibrated before every test to ensure microphone consistency and accuracy. In several cases additional measurements were taken in the same area, either closer to the barrier or higher to determine the e ect of position behind the barrier. At each test site, a microphone was also placed 1 m above the noise wall to measure the unshielded tra c noise so that barrier attenuation could be estimated. In all cases there was a fairly continuous  ow of vehicles travelling at constant speed. Tests were performed in  ve minute intervals for 30 minutes. Noise levels were analyzed in third-octave bands from 20 to 20,000 Hz; total un- and A-weighted levels were also calculated. As the noise source was tra c noise, using the A-weighted tra c noise spectrum was not needed to calculate the A-weighted levels. 395.1. Tra c Noise Consistency (a) (b) Figure 5.1: Average third-octave band Leq and variation (2 ) from all 5 min intervals over a 30 min period at a typical site: a) Un-weighted; b) A-weighted. 5.1 Tra c Noise Consistency Figure 5.1 shows the average un- and A-weighted Leq’s in third-octave bands taken at one site, a result which looked very similar for all other  eld measurements. The dashed lines are the 95% con dence limits, associated with the standard deviation of the six measurements. Above 600 Hz, the results were quite consistent (variation less than  2 dB) suggesting that 5 minutes was a su cient length of time to average variations in tra c noise. Accuracy was the highest (variation of  1 dB) where the A-weighted-spectrum peaked, which was 405.2. Ladner where the noise was perceived to be the loudest. At frequencies below 100 Hz there was quite a lot of variation (up to  5 dB). There was a peak in the spectrum around 1000 Hz, which was typical of tra c noise. 5.2 Ladner Figure 5.2 shows three of the six sites where measurements were taken in Ladner. The foliage in the backyard of 5052, shown in Figure 5.2(a), was cedar and 8-10 m high. The foliage in the backyard of 5040 59A St. (cedar,  10 m high), shown in Figure 5.2(b), was similar to 5052 but was only present above the barrier. The end of 51st St. was the no-foliage case. The un- and A-weighted Leq’s in dB and dBA from these three sites sites, as well as from the unshielded microphone located above the wall, are presented in Table 5.1. The A-weighted Leq above the wall was 15 dBA higher than in any of the protected backyards, suggesting that the barrier attenuated A-weighted levels by at least 15 dBA. Figure 5.3 shows the Leq in third-octave bands, averaged from the six  ve-minute in- tervals for these locations, which were taken simultaneously. All three spectra were similar with little variation above 100 Hz; below 100 Hz the tra c noise was inconsistent, likely explaining the di erence in noise levels occurring there. Above 1100 Hz, noise levels at the two sites with foliage were slightly higher (by up to 2 dB) than at the no-foliage site. Here, some sound was scattered into the shadow zone. The foliages at 5040 and 5052 were quite similar, and therefore the small variation between the two sites was expected. This foliage seemed to have little e ect on the total A-weighted sound levels behind the barriers, with all three sites’ Leq’s being within 1 dBA of each other. 415.2. Ladner (a) 5052 59A St. (b) 5040 59A St. (c) The end of 51st St. Figure 5.2: Three of the test sites in Ladner. Table 5.1: The un- and A-weighted Leq’s from three sites and above the noise wall along Highway 17 in Ladner. Above wall 5052 5040 51st Leq (dB) 86.3 74.0 74.0 75.7 Leq (dBA) 79.6 63.4 64.2 64.2 Figure 5.3: The Leq in third-octave bands averaged over 30 minutes in the backyards of 5052 59A St. and 5040 59A St. and the end of 51st St. 425.2. Ladner Figure 5.4 shows the other three sites where measurements were taken in Ladner. The trees at 5122 59A St., shown in Figure 5.4(a), were deciduous and had broader leaves ( 30 m high, bare trunks to 4 m). The foliage was less dense and less aligned along the wall than in the other yards. The backyard of 5018 59A St., shown in Figure 5.4(b), contained a dense evergreen hedge (cedar,  6.5 m high). 5076 59A St. was the no-foliage case. The un- and A-weighted Leq’s from these sites, as well as from the unshielded mi- crophone located above the wall, are presented in Table 5.2. The A-weighted Leq above the wall was 13 dBA higher than in any of the protected backyards, suggesting that the barrier attenuated A-weighted levels by at least 13 dBA. Figure 5.5 shows the average Leq in third-octave bands for these three sites. The foliages at 5018 and 5122 were quite di erent and so were the Leq levels above 300 Hz. The Leq at 5018 was several dB lower than for the no-foliage case. Here, the foliage was very dense and appeared to back-scatter and absorb sound. The Leq at 5122 was up to 8 dB greater than for the no-foliage case above 1000 Hz, and here the foliage was very tall, broad-leafed and not very dense. There was wind present during the day, possibly causing the foliage to rustle and produce noise. Therefore the higher Leq could be due to both scattering into the shadow zone and wind. The no-foliage case was very similar (within 0.5 dB above 1000 Hz and 3 dB below) to the no-foliage case in the previous set of measurements, suggesting that the tra c noise was fairly constant between the two sets of measurements. At one site, the backyard of 5122, receivers were placed at two di erent distances from the barrier, 3 m and 6 m. The results are shown in Figure 5.6. The Leq in third-octave bands at the position closer to the barrier was approximately 1 dB higher than at the further one. The closer position was deeper into the shadow zone and could therefore be expected to have a lower sound level. However, this result was consistent with treating the di racting edge of a barrier as a secondary source; the Leq was greater when closer to the di racting edge. 435.2. Ladner (a) 5122 59A St. (b) 5018 59A St. (c) 5076 59A St. Figure 5.4: Three of the test sites in Ladner. Table 5.2: The un- and A-weighted Leq’s from three sites and above the noise wall along Highway 17 in Ladner. Above wall 5122 5018 5076 Leq (dB) 86.3 76.7 75.7 77.6 Leq (dBA) 79.6 66.7 62.2 65.3 Figure 5.5: The Leq in third-octave bands averaged over 30 minutes in the backyards of 5018 59A St., 5122 59A St. and 5076 59A St. 445.3. Nanaimo Parkway Figure 5.6: The Leq in third-octave bands averaged over 30 minutes for two barrier-receiver distances in the backyard of 5122 59A St. 5.3 Nanaimo Parkway Figures 5.7(a)-5.7(c) show the three foliage cases studied at the Nanaimo site on Vancouver Island. At the  rst location (N1), a small amount of evergreen foliage, approximately 4 m high, was on the road side of the noise barrier. At the second (N2), there were evergreen trees, approximately 6 m high, behind the microphone on the opposite side than the wall. The third location (N3) was the no-foliage case. The ground was not completely even; therefore the microphone height was measured from the top of the barrier and was kept constant. For all three locations, the microphone was placed 2 m away from the wall and 1.5 m below the top of the wall. At site N1, a second height of 2.3 m from the top was also measured. At site N3, another microphone was placed 1 m above the barrier to approximate the unshielded tra c noise. Table 5.3 shows the un- and A-weighted Leq’s for all three foliage cases at Nanaimo 455.3. Nanaimo Parkway Parkway. The equipment used to calculate levels above the wall only recorded total A- weighted levels, and therefore no unweighted Leq value was obtained. This was the case for all measurements taken above the noise walls on Vancouver Island. Again, the Leq from above the wall was 13 dBA higher than from behind the barrier, suggesting the barrier attenuated levels by at least 13 dBA. Figure 5.8 shows the Leq in third-octave bands averaged from the six  ve-minute inter- vals for the three di erent foliage cases, measured simultaneously. The three levels were quite similar, within 3 dB, up to 1000 Hz. From 1000 to 5000 Hz, site N1, where the foliage was in front of the barrier, had the highest Leq. Location N2, which had the foliage behind the microphone, had the lowest Leq up to 9000 Hz. The no-foliage case was in the middle. The stretch of barrier where these tests took place was on a bend at an intersection, and therefore the three cases were not the same distance to the tra c-noise source, namely Nanaimo Parkway. N1 was the closest to Nanaimo Parkway, then N3 then N2. This could explain the results, which were not expected and did not lead to any signi cance in determining the behaviour of foliage. At site N1 receivers were placed at two di erent heights, 2.3 m and 1.5 m from the top of the barrier. The results are shown in Figure 5.9. The two Leq’s were very similar except around 1000 Hz, where the level at the higher position was approximately 3 dB greater than at the lower position. The lower microphone position was more into the shadow zone and further from the di racting edge, and therefore it was expected that the Leq would be lower there. There was some frequency variation, which suggested possible ground e ects. 465.3. Nanaimo Parkway (a) N1 (b) N2 (c) N3 Figure 5.7: Three test sites along Nanaimo Parkway. Table 5.3: The un- and A-weighted Leq’s from the three foliage cases and from above the wall at the Nanaimo site. Above wall N1 N2 N3 Leq (dB) - 71.7 69.8 71.0 Leq (dBA) 73.2 60.3 57.0 59.5 Figure 5.8: The third-octave band Leq averaged over 30 minutes from three locations along Nanaimo Parkway, measured simultaneously. N1 has foliage in front of the barrier, N2 has foliage behind the microphone and N3 is the no-foliage case. 475.4. Highway 1 and Helmcken Road Figure 5.9: The Leq in third-octave bands averaged over 30 minutes for two receiver heights at site N1: 2.3 m and 1.5 m from the top of the barrier. 5.4 Highway 1 and Helmcken Road Three di erent foliage cases were measured along Highway 1 near Helmcken Road on Vancouver Island, shown in Figures 5.10(a)-5.10(c). At the  rst location (V1), several large broad-leafed trees, approximately 10 m high, were between the barrier and the microphone. Very close by, there was a stretch of approximately 10 m of bare wall with foliage at either end, which was case V2. The third case (V3) was farther down the highway and again had no foliage. However this stretch of bare wall was much longer than in case V2. Here again the ground was quite uneven and therefore the microphone height was measured from the top of the barrier. The microphones were placed 3 m from the barrier and 1.5 m from the top. The microphone was also placed 2.55 m from the top at V1. Again at the no-foliage site, V3, a microphone was placed 1 m above the barrier. Table 5.4 shows the un- and A-weighted Leq’s from all three cases. Here, the A-weighted 485.4. Highway 1 and Helmcken Road Leq from above the wall was 12 dBA higher than from behind the barrier, suggesting the barrier attenuated levels by at least 12 dBA. Figure 5.11 shows the Leq in third-octave bands averaged from the six  ve-minute intervals for the three di erent sites, which were measured simultaneously. As shown in the  gure and in Table 5.4, V3 (the longer no-foliage case) had the highest Leq of the three locations. Above 200 Hz, the Leq of V3 was 5 dB higher than that of V2, the shorter no-foliage case. V1 and V2 were along an on-ramp on the way to the highway, whereas V3 was along the actual highway; therefore the speed of the cars and the volume of tra c along the road could have a ected the noise levels. Above 1000 Hz, the Leq at V1 (the foliage case) was greater than that at V2 by up to 3 dB. This higher frequency noise could have resulted from sound scattering from the broad-leafed foliage into the shadow zone. Below 1000 Hz, back-scattering and absorption of up to 4 dB was seen. The results of V1 and V2 very closely resembled Renterghem et al.’s frequency-dependent results [30]. At site V1 receivers were placed at two di erent heights, 2.55 m and 1.5 m from the top of the barrier. The results are shown in Figure 5.12. Above 1000 Hz, the higher microphone position had levels 1 dB higher than at the lower microphone position. This was to be expected, as the higher microphone position was further out of the shadow zone and closer to the di racting edge. 495.4. Highway 1 and Helmcken Road (a) V1 (b) V2 (c) V3 Figure 5.10: Three test sites along Helmcken Road. Table 5.4: The un- and A-weighted Leq’s from the three foliage cases and from above the noise wall at the Helmcken Road site. Above wall V1 V2 V3 Leq (dB) - 70.7 73.5 74.8 Leq (dBA) 79.6 62.6 61.9 67.3 Figure 5.11: The Leq in third-octave bands averaged over 30 minutes from three locations near Helmcken Road, measured simultaneously. V1 is the broad-leafed foliage case, V2 is the shorter no-foliage case and V3 is the longer no-foliage case. 505.5. Highway 17 and McKenzie Avenue Figure 5.12: The Leq in third-octave bands averaged over 30 minutes for two receiver heights at site V1: 2.55 m and 1.5 m from the top of the barrier. 5.5 Highway 17 and McKenzie Avenue The e ect of vines growing on a noise barrier was investigated along Highway 17 near McKenzie Avenue on Vancouver Island. Measurements were performed along a stretch of wall in two places shown in Figures 5.13(a) and 5.13(b): one where there were vines growing on it and one where there were no vines. There were trees to the sides of and behind the sites. Thus the microphones were placed 1 m from the barrier, and 1.5 m below the top. A microphone was also placed 1 m above the barrier. Table 5.5 shows the un- and A-weighted Leq’s from the vine and no-vine locations. The A-weighted Leq from above the wall was 14 dBA higher than from behind the barrier, suggesting the barrier attenuated levels by at least 14 dBA. Figure 5.14 shows the Leq averaged from the six  ve-minute intervals for the two di erent locations, taken simulta- neously. The Leq at the vine site was lower than that at the no-vine site by up to 5 dB, showing back-scattering and absorption, except between 500 and 1500 Hz. There, the vine site’s Leq was 1-1.5 dB higher. This indicated a small amount of sound scattering from the vines into the shadow zone. 515.5. Highway 17 and McKenzie Avenue (a) Vines (b) No Vines Figure 5.13: The barrier on Highway 17. Table 5.5: The un- and A-weighted Leq’s from the two sites along McKenzie Avenue, vines and no vines, and from the microphone above the wall. Above wall No vines Vines Leq (dB) - 70.4 69.4 Leq (dBA) 73.3 58.6 58.7 Figure 5.14: The Leq in third-octave bands averaged over 30 minutes from the vine and no vine locations at the McKenzie Avenue site, measured simultaneously. 525.6. Summary 5.6 Summary Several test sites were identi ed to test the e ects of foliage near barriers: one site in Ladner, B.C. and several sites on Vancouver Island. Sound levels were measured for 30 minutes in  ve minute intervals behind barriers both with and without foliage nearby. The 30 minute levels for the foliage and non-foliage cases were compared to isolate the e ects of the foliage. Sound levels were also taken above the barriers, giving an unshielded sound level. From this, the approximate barrier attenuation could be determined; attenuations of 12-15 dBA were seen. It was found that  nding ideal test sites was di cult; in several cases there were other e ects in uencing the foliage and the no-foliage cases, making isolating e ects from foliage di cult. In the cases where conclusions could be drawn, it appeared that both back-scattering and absorption, which decreased noise levels, and scattering into the shadow zone, which increased noise levels, occurred. The foliage size, height and density as well as the frequency a ected the impact of the foliage on the performance of the barrier. In the case of tall, broad leafed trees, scattering of up to 8 dB of sound into the shadow zone occurred above 1000 Hz. Dense evergreen hedges appeared to back-scatter and absorb up to 5 dB of sound, while less dense evergreen hedges appeared to have e ects below 2 dB. Vines growing on a barrier also appeared to back-scatter and absorb sound at most frequencies, with e ects up to 5 dB. E ects of changing the position behind the barrier were also examined; it was found that noise levels decreased when the distance from the di racting edge increased. 53Chapter 6 Scale-Model Testing In this chapter, a 1:31.5 scale model, originally developed by Busch [5] was redeveloped and used to examine the factors under investigation: absorptive barriers and foliage near barri- ers. Scale-model materials were selected using excess attenuation measurements and scale- model trees were compared with full-scale foliage. Results of the measurements were then analyzed. Before discussing this work, previous work and theory behind scale-modelling is discussed. 6.1 Previous Work The  rst examination of acoustical scale modelling was in 1934 by Spandock [35]. Early models used fairly low scale factors, such as 8 or 10; however as transducer and recording device technology improved, higher frequencies were able to be studied, and therefore higher scale factors could be used. Scale modelling has been used to study many di erent acoustical environments, including auditoriums, o ces, factories and outdoors. Much focus has been on material selection, which depends on the scale factor as well as the desired full-scale surface. Many studies have been on the e ects of ground surfaces, both with and without noise barriers. These e ects are governed by the impedance of the ground, and therefore it is very important to select a material which accurately models the ground surface of interest. Delany et al. [36] tested various materials as candidates for a scale model at a 1:30 scale. They found that 11 mm thick Insulite softboard covered with a sheet of rough nylon cloth 546.1. Previous Work gave the best excess attenuation associated with grassland. They used sheets of aluminum to model pavement. Hutchins et al. [37] did work on the selection process for scale model materials for a 1:80 scale. They used the same method of determining scale model materials as will be used here (see Section 6.2). Sanded sheets of expanded polystyrene covered with tissue were used for grass, with an e ective  ow resistivity of approximately 300 c.g.s. Rayls/cm. Hutchins et al. used these materials to speci cally study barriers over ground sur- faces [38] at a scale of 1:80. The sound source was a set of ultrasonic whistles, which cover the 10- to 100-kHz range with high amplitude. They used a 1/8 inch Bruel and Kjaer mi- crophone as their receiver. The re ective barriers were made from 1 mm thick aluminum sheets, giving a full-scale thickness of 8 cm. Aluminum sheets were also used to model asphalt and the grass surface developed in [37] was used. The scale model results agreed well with prediction and  eld tests. Horoshenkov et al. [39] explored properties of porous materials to be used for scale modelling at a scale of 1:20. They used the Attenborough impedance model, which uses four independent variables to characterize the materials: porosity, tortuosity,  ow resistivity and layer depth. They mainly examined the frequency dependence of the impedance, but also looked at the angular dependence. They found that rubber-backed carpet best modelled asphalt and a  berglass surface best modelled dry sand. Hutchins et al., using the setup described previously, also studied parallel barriers [40]. A four lane highway with a central grass section was created and several source and receiver positions were studied. The barriers were 4.9 m tall and placed 35 m away from each other. They found that re ections from the face of the second barrier were only signi cant when the source was placed near that second barrier. Pirinchieva [41] used a 1:20 scale model to study sound propagation behind barriers of  nite length. He used a point source for a frequency range of 5-20 kHz, and used a 1/4 inch 556.1. Previous Work B&K microphone as a receiver. The ground was modelled using painted plywood and the barriers were made of 5 mm thick polystirol plates stuck on 4 mm glass and then painted. Some work has already been done to study absorptive noise barriers using scale mod- elling. Osman [42] developed a 1:16 scale-model facility, later used to study di erent shapes of noise barriers, both re ective and absorptive [9]. Menge [43] studied the e ects of us- ing sloped barriers instead of absorption to reduce ampli cation between parallel barriers using a 1:30 scale model. Trucks were the dominant source of noise in the speci c case he was working on, therefore the 250, 500 and 1000 Hz octave bands were studied. He used 16 mm medium-density overlay plywood with smooth, dense paper glued to both sides to model concrete, asphalt, brick and steel, as well as the re ective sloped barriers. He used  berglass for the absorptive barriers. He used an electric spark discharge as an impulsive sound source and a 1/4 inch microphone as the receiver. Hothersall et al. [44] used a scale model at a scale of 1:20 to test re ective and absorptive railway noise barriers. They used a polished aluminum surface to simulate rigid ground and used specially manufactured, 8 mm thick porous plastic plates to simulate grass. The barriers were modelled using plastic or steel and were made absorptive by adding a layer of felt. Busch [5] created a scale model to investigate noise walls, earth berms, and a com- bination of the two. He used an air-jet noise source and performed excess attenuation experiments to determine both the optimal scale factor and the materials to be used. He chose a scale-factor of 31.5 and created the model in an anechoic chamber. He tested the anechoic chamber thoroughly and determined it was an appropriate testing environ- ment for the scale model. He used varnished particle board to model roadways, dense polystyrene to simulate noise walls, and expanded polystyrene to model soft ground and earth berms. He used felt and expanded polystyrene to make the earth berms softer and harder, respectively. 566.2. Theoretical Considerations 6.2 Theoretical Considerations When building an accurate scale model, there are many factors that must be taken into consideration. For a scale factor n, all dimensions and distances are scaled by 1=n. The speed of sound remains the same in the scale model, so to ensure that the relation between distances and the acoustical wavelengths remain constant the wavelength  must become  =n; therefore the frequency f must be scaled up to nf . Issues occur at these higher frequencies, such as air absorption becoming very signi cant (See Section 6.2.1 for the cal- culations). Another issue which needs to be taken into account is  nding an approximately omni-directional sound source which has a fairly constant power output up to 100 kHz. The directionality of the microphones is also a problem, as one wants the microphone to be as omni-directional as possible, and therefore the smallest microphones available must be used. Furthermore, because the wavelengths of the frequencies of interest are so small, the protection grid on the microphone must be accounted for, as it is no longer a negligible size at these frequencies and may a ect the frequency response. It is assumed here that e ects such as di raction and interference are consistent under scaling. Selecting appropriate scale-model materials is crucial to the accuracy of a scale model. The method of selection here was used by Hutchins et al. [37]. Materials to be used in an acoustical scale model must be found which have the same acoustical impedance at scaled up test frequencies as real-world materials do at full-scale frequencies. The impedance of a  brous material is given using the Delany-Bazley model [45]: Z = 1 + 9:08  f    0:75 + i11:9  f    0:73 ; (6.1) where  is the  ow resistivity in c.g.s. Rayls/cm. Since the frequency is scaled by the scale factor n in the model measurements, the  ow resistivity must also be scaled by n to keep Z constant. It is the  ow resistivity divided by the scale factor n, called the e ective  ow 576.2. Theoretical Considerations resistivity, which is compared to real-world values. To calculate the surface impedance, and therefore the  ow resistivity, of a material, the excess attenuation (EA) must be measured. Excess attenuation measurements involve a source and receiver in a known con guration above a material of interest and measuring the sound pressure level. From this, the EA is calculated by: EA = Lp;surface  Lp;ff ; (6.2) where Lp;ff is the free- eld pressure level, with the scaled source-receiver distance taken into account when correcting for air absorption and divergence. Once the measurements are taken, a least-squares  t is performed to  t the average measured EA to the EA predicted for the di erent  ow resistivity values (for the pre- dicted EA calculation, see Section 6.2.2). By this method, the e ective  ow resistivities of materials are determined and then compared to values for full-scale materials and chosen accordingly. 6.2.1 Air Absorption In this section, the calculation of the air absorption coe cient  A is shown, as done by Bass et al. [46]. The ANSI standard on the measurement of air absorption [47] gives the air absorption coe cient for still air in nepers per meter as:  A = f 2  1:84 10 11  ps0 ps   T T0  1=2 +  T T0   5=2 1:278 10 2 e 2239:1=T fr;O + (f 2=fr;O) + 1:068 10 1 e 3352=T fr;N + (f 2=fr;N)  ; (6.3) where ps0 is the reference atmospheric pressure (1 atm), ps is the atmospheric pressure, T is the atmospheric temperature in K and T0 is the reference atmospheric temperature (293.15 K). fr;O and fr;N are the relaxation frequencies of molecular oxygen and nitrogen 586.2. Theoretical Considerations respectively, given as: fr;O =  ps ps0   24 + 4:04 104h 0:02 + h 0:391 + h  (6.4) fr;N =  ps ps0   T0 T  1=2  9 + 280he  4:17  (T0T ) 1=3  1  ! ; (6.5) where h is the molar concentration of water vapour in percent. This is calculated from the relative humidity hr, by: h = hr  psat ps0   ps0 ps  : (6.6) The fraction of the saturated vapour pressure psat over the ambient pressure ps0, as done by Bass et al. in a later paper [48], is: log10  psat ps0  =  6:8346  T0 T  1:261 + 4:6151: (6.7) The conversion 1 Np  8.686 dB is used to obtain the air absorption coe cient in decibels per meter. 6.2.2 Excess Attenuation Prediction In this section, a model to predict the excess attenuation of a ground surface will be developed. The velocity potential above a surface is calculated given a speci c source and receiver geometry. Scale model materials will be chosen based on their excess attenuations compared to those of the full scale materials they are modelling. The excess attenuation can be predicted from the velocity potential  and the free- eld velocity potential  0 using: EA = 20 log    0  : (6.8) The derivation of the velocity potential assumes a time dependence of e i!t. The math 596.2. Theoretical Considerations behind this derivation is presented in [49]. The derivation has been done in detail in [50], [51], [52] and [53]. The source and receivers are assumed to be dimensionless points. The ground surface is assumed to be locally-reacting with a normalized admittance of  =  c=Z. The geometry is de ned by the source height, h1, the receiver height, h2, and the source- receiver distance, d. The direct and re ected source-receiver distances are denoted r1 and r2 respectively, and are calculated by: r1 = p d2 + (h2  h1)2 (6.9) r2 = p d2 + (h2 + h1)2: (6.10) The grazing angle  , the angle the re ected path makes with the impedance plane, is calculated by:  = arctan  h1 + h2 d  : (6.11) The complex plane-wave re ection coe cient Rp, assuming locally-reacting ground, is given by: Rp = sin   sin +  : (6.12) The spherical-wave re ection coe cient is de ned as: Q = Rp + (1 Rp)F (w); (6.13) where F (w) is called the spherical-loss factor and is given by: F (w) = 1 + i p  w e w 2 erfc( iw); (6.14) 606.2. Theoretical Considerations and w is the numerical distance, calculated by: w =  1 + i 2  p r2k (sin +  ); (6.15) where k is the wavenumber in air. The importance of choosing the correct square root of i in the equation for w, here presented in the proper form 1+i2 , is discussed by Stinson [54]. By de ning f(w) as a modi ed form of the complementary-error function: f(w) = e w 2 erfc( iw); (6.16) Equation 6.14 can be rewritten as: F (w) = 1 + i p  w f(w): (6.17) The velocity potential is then de ned to be:  = eikr1 4 r1 +Q eikr2 4 r2 : (6.18) The free- eld velocity potential  0 is de ned for when there is no re ected component, so when Q = 0. The  nal step is the calculation of the modi ed complementary-error function: f(w) = H(y; x) + iK(y; x); (6.19) where x and y are the real and imaginary parts of the numerical distance w respectively. A new constant h is introduced, related to the error bound Eh on calculating f(w), de ned to be: Eh = 2 p  e  2=h2 1 e  2=h2 : (6.20) Smaller values of h reduce the value of the error bounds, leading to more accurate calcu- 616.2. Theoretical Considerations lations; h = 1 is su cient for the calculations here. Four new variables are de ned for the derivation of the terms in Equation 6.19: A1 = cos(2xy) (6.21) B1 = sin(2xy) (6.22) C1 = e  2 y=h  cos(2 x=h) (6.23) D1 = sin(2 x=h): (6.24) Using these variables, two new terms are calculated: P2 = 2e  (x2+(2 y=h) y2)A1C1  B1D1 C21 +D 2 1 (6.25) Q2 = 2e  (x2+(2 y=h) y2)A1D1 +B1C1 C21 +D 2 1 : (6.26) The real and imaginary parts of the error function in Equation 6.19 are de ned by the following equations: H(y; x) = hy  (y2 + x2) + 2yh  1X n=1 e n 2h2(y2 + x2 + n2h2) (y2  x2 + n2h2)2 + 4y2x2  yEh pi + P2;final (6.27) K(y; x) = hx  (y2 + x2) + 2xh  1X n=1 e n 2h2(y2 + x2  n2h2) (y2  x2 + n2h2)2 + 4y2x2 + xEh pi  Q2;final; (6.28) where P2;final and Q2;final are de ned by comparing y to  =h. If y <  =h then P2;final = P2 and Q2;final = Q2; if y =  =h then P2;final = P2=2 and Q2;final = Q2=2; otherwise P2;final = 0 and Q2;final = 0. 626.3. Experimentation 6.3 Experimentation A 1:31.5 scale model, developed by Busch as part of his Masters research [5], was redevel- oped here. The scale-model measurements were performed in an anechoic chamber with dimensions 4.1 m x 4.7 m x 2.6 m. A 1/4" Bruel & Kjaer type 4135 free- eld microphone was used as the receiver, with a Bruel & Kjaer type 2669 pre-ampli er and an adaptor for a 1/2" pre-ampli er to a 1/4" microphone. A B&K Nexus Conditioning Ampli er was used mainly for cable-adapting, and was set as a high-pass  lter with a cut-o frequency of 20 Hz. The output sensitivity of the ampli er was set to 31.6 mV/Pa. A Stanford Re- search Systems SR-770 FFT Network Analyzer was used to average and record the acoustic signal in 400 spectral bins, 250 Hz wide, from 0-250 Hz up to 99,750-100,000 Hz. Each measurement took 2000 spectral averages. The results were stored on 3.5"  oppy disks and analyzed in MATLAB. In order to calculate the air absorption, the temperature and humidity were measured with a Psychro-Dyne psychrometer. 6.3.1 Air-Jet Source The sound source used here was the air-jet source used and tested in Busch’s thesis [5], who provided a detailed description and the results of in-depth tests of the source in the anechoic chamber. Presented here is a brief description and an examination of several of the source’s properties. The air-jet source was developed from the description by Novak [55], designed speci - cally for scale-model tra c noise. An ideal source must have su cient power output for a broadband spectrum up to 100 kHz. The source was made of six co-planar jets, each with a diameter of 0.3 mm, spaced at 60o intervals around a cylinder with a diameter of 6.5 mm. The outer housing and the core piece, shown in Figure 6.1, were both made of brass. The core piece had resonant cavities which ampli ed the source power at lower frequencies. 636.3. Experimentation Figure 6.1: The air-jet source. (1) The outer housing. (2) O-ring, size no. 15. (3) The core piece. [5] Protection Grid At very high frequencies, the microphone protection grid is no longer a negligible size in comparison to the wavelength. Therefore, the e ects must be taken into account when cal- culating the sound pressure level. The correction on the sound levels due to the protection grid was determined by measuring the sound pressure level 1 m from the source, both with and without the protection grid (PG). The correction was then calculated by:  Lmicrophone = LPGoff  LPGon: (6.29) LPGoff and LPGon are shown in Figure 6.2. All measurements were subsequently taken with the protection grid on and corrected, in order to protect the microphone. Source Power Output To determine the sound power level of the source, the sound pressure level was measured at eight di erent distances from the source, from 0.4 m to 2 m. The sound source was oriented vertically and the microphone was oriented horizontally, pointing towards the source. From 646.3. Experimentation Figure 6.2: The sound pressure level measured at 1 m from the source, with and without the protection grid. the sound pressure level Lp, the sound power level Lw was determined by: Lw = Lp + 20 log(r) + 10 log(4 ) +  Lair +  Lmicrophone; (6.30) where r is the source-receiver distance,  Lair is the air absorption correction, and  Lmicrophone is the microphone response correction due to the protection grid. The average Lw, shown in Figure 6.3, was calculated from the eight measurements at di erent source-receiver po- sitions. Source Inclination Angle The e ect of varying the inclination angle of the sound source was measured, by varying the angle while measuring the sound pressure level 1 m away from the source. 0o was de ned to be the air-jet stream pointing directly towards the microphone, while 90o was de ned to be when the air-jet stream was perpendicular to the microphone. The sound 656.3. Experimentation Figure 6.3: The sound power level of the air-jet source. pressure level was then corrected for air absorption and protection grid response. Figure 6.4 shows the sound pressure level as a function of source inclination angle and frequency. As the angle approached 90o, the high frequency power dropped o considerably, and the low frequency power increased sharply. This sharp increase was due to the air-jet stream directly hitting the microphone. From 0o up to 50o the spectrum was quite  at, and therefore the scale model measurements were limited to these angles. 6.3.2 Frequency Range All subsequent measurements were performed using scaled frequencies, then the frequencies were scaled down over the full-scale range. Using a scale factor of 31.5 meant the frequency range over which measurements were performed was 1390 to 89100 Hz, corresponding to the range of the full-scale 63 Hz to 2000 Hz octave bands. Octave band results were calculated 666.3. Experimentation Figure 6.4: The sound pressure level varying with both source inclination angle and fre- quency. from the 400 frequency bins, using: Lp;band = 10 log10  m2X i=m1 10Lp;i=10 !  10 log10(m2  m1 + 1); (6.31) where m1 and m2 are the  rst and last bin numbers included in the band. 6.3.3 Excess Attenuation Measurements Excess attenuation measurements were performed in Busch’s thesis [5] to determine the  ow resistivity of candidate scale-model materials. An error found in the thesis, dividing the e ective  ow resistivity by the scale factor to obtain an incorrect e ective  ow resistivity (corrected in a later paper [56]), led to the scale-model selection process being repeated here. EA measurements were performed, as described in Section 6.2. The full scale con gu- ration used for these measurements was as follows: source height of 0.5 m, receiver height 676.3. Experimentation Table 6.1: E ective  ow resistivities  eff for full-scale materials. Ground  eff (c.g.s. Rayls/cm) Absorptive barrier 30-60 Grass 150-300 Loose-packed dirt 300-800 Asphalt roads 30,000 Concrete barrier 30,000-100,000 of 1.8 m and a source-receiver distance of 30 m; the source was pointing straight down in order for it to be as omni-directional as possible. The source and receiver heights were those used later in the insertion loss tests. Three measurements were taken for each surface, to average out any irregularities in the material. Several full-scale materials were to be modelled: asphalt roadways, loose-packed dirt (highway shoulders), concrete (re ective) noise barriers and absorptive noise barriers. Ta- ble 6.1 gives the e ective  ow resistivities of these surfaces, all but the absorptive barrier given by Embleton et al. [57]. The absorptive barrier  ow resistivity was determined by comparing the full-scale commercial barrier absorption coe cients with the calculated ab- sorption coe cient using the Delany-Bazley model. Several materials were tested to model these surfaces: a fuzzy blanket, felt, green fabric, one and two layers of linen, 3/4" plywood, varnished particle board, and 3 mm thick dense plastic. The results of the EA measurements, and the best- t EA prediction curves for each material, are shown in Figures 6.5(a)-6.6(d). The e ective  ow resistivities are listed in Table 6.2. The EA curves for materials with very high  ow resistivities did not appear to have a distinct minimum. The minima for these surfaces could be above the frequency range and 686.3. Experimentation (a) (b) (c) (d) Figure 6.5: The excess attenuation measurements and best- t predictions for a) the fuzzy blanket ( eff = 33 c.g.s. Rayls/cm), b) felt ( eff = 64 c.g.s. Rayls/cm), c) the green fabric ( eff = 253 c.g.s. Rayls/cm), and d) two layers of linen ( eff = 430 c.g.s. Rayls/cm) therefore were not measured. The EA curves for one and two layers of linen had minima, but then at high frequencies did not rise as much as the predicted curves. The Delany- Bazley model is valid only for  brous, absorptive material, and therefore the prediction model breaks down for higher  ow resistivities and non- brous material. Due to the lack of distinct minima and the deviation from the model, especially at high frequencies, only full-scale frequencies up to 1500 Hz were considered when performing the least-squares  t. By comparing the  ow resistivity values, scale model materials were chosen. Asphalt was modelled by plywood, the roadside was modelled by two layers of linen, the green fabric 696.3. Experimentation (a) (b) (c) (d) Figure 6.6: The excess attenuation measurements and best- t predictions for a) linen ( eff = 1; 550 c.g.s. Rayls/cm), b) plywood ( eff = 14; 600 c.g.s. Rayls/cm), c) dense plastic ( eff = 20; 000 c.g.s. Rayls/cm), and d) varnished particle board ( eff = 40; 000 c.g.s. Rayls/cm). modelled grass, the dense plastic modelled the re ective barriers and the fuzzy blanket was added to the source side of re ective barriers to make them absorptive. Using the e ective  ow resistivity of the fuzzy blanket, the e ective absorption coe - cient was calculated with the Delany and Bazley model. The e ective absorption coe cient at full scale frequencies is shown in Figure 6.7. This was similar to the results of the spher- ical decoupling and impedance tube tests performed on the full scale absorptive material. 706.3. Experimentation Table 6.2: E ective  ow resistivities  eff for scale model materials. Material  eff (c.g.s. Rayls/cm) Fuzzy blanket 33 Felt 64 Green fabric 253 Two layers of linen 430 One layer of linen 1,546 Dense plastic 20,000 Plywood 35,500 Varnished particle board 370,000 Figure 6.7: The e ective absorption coe cient at full scale frequencies of the fuzzy blanket, calculated using the Delany and Bazley model. 716.3. Experimentation Figure 6.8: The scale-model tree. 6.3.4 Scale-Model Trees Scale-model trees, shown in Figure 6.8, were used to model tree foliage. The trees were 17.5 cm tall, corresponding to a full-scale height of 5.5 m. To characterize the foliage, scattering and absorption by the trees were measured. The sound source, at a full-scale height of 1 m, was located over grass, modelled by the green fabric, 10 m away from a line of trees. Receivers were placed 5 m in front of and 5 m behind the row of trees, at a height of 1 m. The sound pressure level (SPL) was measured at both receiver positions, with and without the row of trees present. From this, the tree insertion loss could be calculated, by subtracting the SPL with the trees from that without the trees. This measurement was repeated at full-scale, on a hedge along the length of Wolfson Field, a rugby  eld on the UBC campus. Figure 6.9 shows a picture of the hedge. The insertion losses from both the scale-model measurements and the full-scale measurements are presented in octave bands in Figure 6.10. There were some similarities and some large di erences between the scale-model and 726.3. Experimentation Figure 6.9: The evergreen hedge along Wolfson Field. the full-scale  eld results. Attenuation through the foliage was seen in both cases: the trees attenuated sound by up to 3 dB in the scale-model tests and 5 dB in the full-scale tests, due to scattering or absorption. The IL in the  eld test was up to 2 dB smaller than the scale-model results below 600 Hz and higher by up to 2 dB above 600 Hz. In the scale-model results, the trees had very little e ect on the receiver in front of the trees. In the  eld tests, however, sound levels actually decreased in front of the barrier when the trees were present. One reason for this was the change of ground surface between measurements. The tests in the no trees case were done in the middle of a grass  eld, while the ground beneath the hedge contained roots which added porosity, increasing the ground absorption. This could also increase the appearance of attenuation due to foliage in the results taken behind the trees. In the scale-model measurements, the ground remained the same, as the removal of the trees did not a ect the ground. Another reason for the di ering results is the leaf size; the leaves in the full-scale hedge were much smaller than those in the scale-model trees. The full-scale tests were done on an evergreen hedge, and therefore the leaves were very small. In contrast, the leaves 736.3. Experimentation Figure 6.10: The measured IL in octave bands of a row of trees, measured 5 m in front of and 5 m behind the foliage. Full-scale  eld measurements (FS) are compared with scale-model measurements (SM). on the scale-model trees were quite large compared with the wavelength; the leaves were approximately 2 mm wide, corresponding to a full scale size of 6 cm. This would be a closer model to a broad-leafed tree or hedge. It was attempted to locate such a hedge for testing; however an appropriate one could not be found. The small change due to foliage seen in front of the hedge, in the scale-model measure- ments where the ground was consistent, and the much greater decrease in sound which reached the back suggested that energy was being scattered or absorbed by the foliage, while little was being back-scattered. The foliage absorbed energy by transferring the sound energy into vibrational energy of the leaves and branches. Sound that was scattered was sent in many directions, as opposed to transmitting through to the receiver on the other side of the foliage. 6.3.5 Insertion Loss Tests The e ects on barrier performance of two factors were examined using the acoustical scale model: barrier absorption and tree foliage. Both single and parallel barriers were used to 746.3. Experimentation Figure 6.11: The parallel-barrier con guration. The barrier height varied, with h having values of 3, 4 and 5 m. Dimensions are shown using full-scale equivalent distances. investigate these e ects. In both con gurations, described here using the corresponding full-scale dimensions, a 22 m wide, four-lane highway was modelled. The shoulder, the space between the asphalt and the barrier, was 4 m wide. A distance of 30 m between the parallel barriers was chosen due to the facts that a smaller distance is rarely found in the  eld and that the ampli cation e ects are reduced at larger distances. The sound source was placed 0.5 m high, in the center of the highway, 11 m from the shoulder. Receivers were placed 5, 10, 15 and 20 m behind the barrier(s) at a height of 1.8 m. Barrier heights of 3, 4 and 5 m were tested. Figure 6.11 shows the full-scale test con guration with parallel barriers, and Figure 6.12(a) is a photo of the setup with re ective parallel barriers. (a) (b) Figure 6.12: The experimental setup of the scale model in the anechoic chamber with parallel barriers on either side of the air-jet source. a) Re ective Barriers. b) Absorptive Barriers. 756.3. Experimentation Figure 6.13: The measured IL in octave bands at receiver position R2 for the 5 m high re ective parallel barriers. Absorption The e ects of barrier absorption on the source side of the barrier were examined for three di erent barrier heights: 3, 4 and 5 m. Several con gurations were measured: re ective and absorptive single barriers, re ective and absorptive parallel barriers, and parallel barriers with one re ective and one absorptive. In the last of these con gurations, the re ective barrier was the one between the source and receiver positions R1-R4, while the one between the source and positions R5-R8 was absorptive. Figure 6.12(b) shows a picture of the absorptive parallel barriers. When testing one barrier, the barrier between the source and receivers R5-R8 was removed; the IL’s for those tests at those receivers were close to zero and are not shown. Figure 6.13 shows the octave band IL at receiver position R2 for the 5 m high re ective parallel barriers. IL varies with frequency from 11-16 dB, due to complex ground inter- actions. Figure 6.14 shows the IL di erences between the re ective parallel barriers and the other barrier and absorption con gurations. The IL shown in Figure 6.13 has been subtracted from the IL’s for the other con gurations; therefore a positive change in IL is 766.3. Experimentation Figure 6.14: The measured di erence in IL between re ective parallel barriers and the other con gurations. Shown in octave bands and measured at receiver position R2 for the 5 m high barriers. a decrease in noise levels and an improvement in barrier performance. At low frequencies, the e ect of adding a second barrier is apparent; the IL was up to 2 dB higher for a single barrier than for parallel barriers. Here, absorption increased IL by 1 dB for the parallel barriers. At high frequencies, adding absorption to a single barrier increased IL by 0.5 dB. For parallel barriers, making them absorptive increased IL by up to 2.5 dB. Adding absorption to one of the parallel barriers improved IL slightly; however the IL was still slightly lower than a single re ective barrier. The A-weighted IL’s for the di erent con gurations at each receiver position, and for a barrier height of 5 m, are shown in Figure 6.15. Changing from a single 5 m re ective barrier to 5 m parallel re ective barriers decreased the IL by approximately 1 dBA. This demonstrates the ampli cation that occurs between parallel barriers. When using absorp- tive barriers, the parallel barriers gave IL’s which were very similar to those of a single barrier. Absorption added to the re ective walls increased the IL very slightly (< 0:2 dBA), but reduced re ections from the wall by up to 1 dBA. 776.3. Experimentation Figure 6.15: The measured A-weighted IL’s for the 5 m tall barriers at the eight receiver positions. Figure 6.16 shows the A-weighted IL’s for parallel barriers at receiver position R2 for the three barrier heights. Based on these results, increasing the height of a barrier by 1 m increased the IL by more than adding absorption to a smaller noise barrier. By  tting a line through the data points, it was determined that adding absorption had the same e ect on IL as increasing the barrier height by 0.33 m. Figure 6.16: The measured A-weighted IL’s for absorptive and re ective parallel barriers at R2 for the three di erent receiver heights. 786.3. Experimentation Figure 6.17: The measured change in IL in the case of parallel barriers with and without a line of trees along the source sides of the barriers. Shown in octave bands and measured at receiver R2 for 5 m high parallel barriers. Foliage: Parallel Barriers Figure 6.17 shows the e ect of adding a row of trees along the source sides of 5 m high parallel barriers. The trees were approximately 5.5 m high, so they overtopped the wall slightly. The measured change in IL in the case of re ective barriers with and without the rows of trees is shown in octave bands, measured at position R2. The foliage had negligible e ect up to 500 Hz, then decreased the IL at frequencies up to 1250 Hz. Above this the foliage increased IL, acting as a scatterer; sound that would normally re ect from one barrier and di ract around the other is scattered in other directions. Below 1250 Hz, the foliage which overtopped the barrier scattered sound into the shadow zone, causing the decrease in IL. Figure 6.18 shows the total A-weighted IL of re ective and tree-lined parallel barriers at all receiver positions. The trees on the source sides of the barriers decreased the total IL by up to 1 dBA. The increase observed at high frequencies is not enough to balance the decrease below 1250 Hz. 796.3. Experimentation Figure 6.18: The measured A-weighted IL’s for the 5 m tall barriers at the eight receiver positions, with and without a line of trees along the source sides of the barriers. Foliage: Single Barrier The e ects of foliage at di erent positions around the barrier were examined using a single, 3 m high barrier. Only four receiver positions, R1-R4, were behind the single barrier, therefore measurements were taken only at those four positions. The trees were placed at di erent positions around the barrier: directly behind the barrier, directly in front of the barrier, and 10 m behind the barrier such that receiver position R1 is between the trees and the barrier. Two di erent foliage heights were used: 5.5 m and 7.2 m. For the taller trees, both the regular density of trees, where the tree bases were placed approximately 1.5 m apart, and a thicker row of trees, where tree bases were placed 0.9 m apart, were tested. Figure 6.19 shows the taller, denser foliage placed behind the barrier. The di erences in IL between a re ective wall and the di erent foliage con gurations are shown in Figures 6.20 and 6.21 for the shorter and taller trees, respectively. Placing the foliage directly next to the barrier, either in front or behind, had little e ect at low 806.3. Experimentation Figure 6.19: Taller, denser foliage behind the barrier. frequency and caused an increase in IL at mid-frequencies. Here the sound was absorbed and back-scattered by the foliage. At high frequencies, the IL decreased by up to 4 dB. At these frequencies, sound was scattered by the foliage into the shadow zone. For taller trees, the attenuation at lower frequencies was greater, and scattering into the shadow zone began to occur at a lower frequency. At low frequencies, the taller trees provided more opportunity for sound absorption and back-scattering, much like increasing the height of a noise barrier. At higher frequencies, there was more e ective foliage surface area to scatter the noise. The foliage had very little e ects on the total A-weighted IL values; the low frequency increase and high frequency decrease in general averaged out. Placing the trees behind the receiver position had very little e ect on the IL, in agree- ment with earlier tests that found little sound is back-scattered from a row of trees. Using denser foliage also had a small e ect on the IL. In general, IL increased very slightly, meaning that the denser foliage attenuated more sound, which was to be expected. 816.3. Experimentation Figure 6.20: The measured change in IL between a re ective barrier and the di erent foliage con gurations. Shown in octave bands at receiver R1 for a 3 m high barrier, with 5.5 m tall trees. Figure 6.21: The measured change in IL between a re ective barrier and the di erent foliage con gurations. Shown in octave bands at receiver R1 for a 3 m high barrier, with 7.2 m tall trees. 826.4. Summary 6.4 Summary A scale model was developed to test factors which a ect highway noise barriers. Excess attenuation measurements were performed to select appropriate model materials. The parameter  ow resistivity was used and the Delany-Bazley model was assumed, which is not valid for acoustically hard materials. A four-lane highway con guration was then set up, with the option of having a single barrier or parallel barriers. Absorptive barriers were investigated using barriers of varying height. It was shown that adding absorption to the source side of parallel barriers increased the total IL by 1 dBA, which was found to be equivalent to increasing the height of the barrier by 0.33 m. It was also seen that using absorptive barriers prevented the 1 dBA decrease in IL when adding a second barrier that occurred with re ective barriers. The e ects of tree foliage near barriers were also examined using the scale model. Measurements done on the scale-model trees were compared with the same measurements done at full scale on an evergreen hedge, where the results varied by up to 2 dB. This could indicate that there is another material which would better model an evergreen hedge and that the model trees used model a di erent type of foliage more accurately, such as a broad-leafed tree. These trees were placed in di erent positions near the barrier, as seen in the  eld. It was seen that foliage directly in front of or behind the barrier scattered up to 4 dB of sound into the shadow zone above 1000 Hz, causing the barrier to be less e ective at these frequencies. It was also seen that foliage attenuated up to 2 dB of sound at mid-frequencies, increasing the e ectiveness of the barrier. 83Chapter 7 Prediction This chapter discusses the prediction of the e ects of absorption and vegetation on barrier performance. Three prediction methods were used: ray tracing,  nite elements and the method of images. Two di erent di raction algorithms were used: the Uniform Theory of Di raction and Svensson’s model. The results from the full-scale anechoic chamber testing (Chapter 4) were predicted using all three prediction methods in hopes of validating the prediction models. The foliage characterization tests done for the scale-model trees (Section 6.3.4) were then predicted using ray tracing. The following sections will go into the details of both di raction models as well as each prediction method, and then the results will be shown and discussed. 7.1 Edge Di raction Di raction is the bending of sound waves around an edge. It is the mechanism that allows sound to reach the shadow zone behind a barrier; therefore the accuracy of the di raction model is crucial when modelling outdoor noise barriers, where the di raction paths contribute all of the sound at a receiver position. Two theories of di raction were used here: the Uniform Theory of Di raction and Svensson’s model. Keller [58] developed the Geometric Theory of Di raction (GTD), a frequency-domain model which calculates a complex di raction coe cient for electromagnetic waves travelling over an in nitely long, perfectly conducting wedge. The di raction coe cient depends on the geometry of the wedge and the source and receiver positions. His work was an extension 847.2. Ray Tracing of geometrical optics, where the wavelength of interest is very small; therefore the theory is only valid at high frequencies. Kouyoumjian and Pathak [59] modi ed the GTD to create the Uniform Theory of Di raction (UTD). This method is valid for the shadow and re ection boundaries, where Keller’s theory had singularities. Further prediction work has been done using the UTD by Kawai [60], who extended the UTD to study many sided barriers, and Tsingos et al. [61], who studied the modelling of virtual environments using beam-tracing. Biot and Tolstoy [62] developed a time-domain model, studying the impulse response of a di racted spherical sound wave by a rigid wedge. Medwin [63] went on to study the Biot-Tolstoy model when applied to noise-barriers and found good agreement in the case of in nite edges. He extended the model to account for  nite-length wedges and used the concept of a secondary edge source. Svensson et al. [64] further extended Medwin’s work to form a new impulse-response model. They used line-integrals to model the edge, which removed a singularity found in the Biot-Tolstoy model. In a later paper [65], Svensson et al. went on to remove a di erent type of singularity from the Biot-Tolstoy model, along the specular-zone and shadow-zone boundaries. More work was then done [66] to transform the model to the frequency domain. The theory of both the UTD and Svensson’s model are presented in Appendix A. 7.2 Ray Tracing The ray tracing program used, PRAY, was developed by Hodgson et al. [67], originally based on the energy algorithm developed by Ondet and Barbry [68]. A source emits a number of rays in random directions, each with an equal amount of initial sound pressure (using the phase model) or pressure squared (using the energy model). Each ray’s trajectory is followed as it travels in a straight line until it encounters an obstacle, where it is re ected, either specularly or di usely. An obstacle may be a wall or a scattering obstacle de ned by 857.3. Method of Images a volume of randomly distributed scatterers. Each obstacle has a de ned complex re ection coe cient, which reduces the amount of energy the ray contains, as well as the phase of the ray. A wall may also re ect di usely, controlled by a user-de ned di usion coe cient. The ray’s energy and pressure can also decrease due to propagation over a distance and air absorption. A plane of cubic receivers is de ned, and the pressure and energy of all rays which pass through each receiver are accumulated to give the total sound pressure level. Di raction was included in PRAY by Chan in 2007 [69] using the UTD. Yousefzadeh [70] considered Svensson’s model as an alternate method of di raction using beam-tracing. However, this was never integrated into PRAY, but was implemented as part of an image method. His implementation was modi ed and integrated into PRAY here. Predictions were performed using both the UTD and Svensson’s model. Because each ray in in nitely thin, one will almost never hit the tip of an edge exactly. Therefore if a ray hits an obstacle within half of a wavelength to the edge, it will di ract. This value was decided on by Chan [69], who performed anechoic chamber measurements. 7.3 Method of Images In the simplest case, where a source and receiver are placed above a re ecting surface, the method of images (MOI) re ects the source in the surface and treats it as a second (image) source. The sound level at the receiver is then the sum of the direct sound from two sources: the real source and the image source. When a barrier is inserted between the source and receiver, there are four paths to consider instead of two, re ecting both the source and the receiver in the ground, as shown in Figure 7.1. The image source accounts for the re ected path on the source side, while the image receiver accounts for the re ected path on the receiver side. This method assumes that the surface is perfectly re ecting; however  nite-impedance surfaces can be modelled approximately [71]. The pressure components from the image 867.4. Finite Element Method Figure 7.1: The four sound paths between a source and a receiver with a barrier in between. The method of images uses an image source and image receiver to model the re ected paths. source or reaching the image receiver are multiplied by the re ection coe cient of the surface before the sound levels from the four paths are summed. 7.4 Finite Element Method The  nite element method (FEM) is a numerical method which solves di erential equations, de ned over a relatively simple domain with de ned boundary conditions. It is useful for acoustics in a well-de ned space, because the governing di erential equation, the wave equation, is fairly straight forward. A mesh is created, where the domain is split up into a number of elements; the number of elements needed for an accurate solution is dependent on the wavelength of interest, and the accuracy will diminish if there are not a su cient number of elements per wavelength. Run times and computer memory become problems for larger domains and higher wavelengths; therefore only the full-scale anechoic chamber results at 1000 Hz were predicted, in two dimensions. Here the domain is fairly small | 877.4. Finite Element Method 4.6 m wide by 2.6 m high | and the wavelength corresponding to 1000 Hz is 0.34 m. The  nite element code used here was created in MATLAB by the author for a course project at the University of British Columbia. The wave equation, de ned over the two-dimensional domain  with appropriate bound- ary conditions de ned on the boundary @ , is given by: r2p+ k2p = f(x; y) on  rp  n = ik Z p on @ ; (7.1) where p is the pressure, k is the wavenumber, Z is the impedance and r2 is the two- dimensional Laplacian operator using Cartesian coordinates. f(x; y) is the source function, given by: f(x; y) = C  (x x0; y  y0) (7.2) where C is a constant which depends on the source strength and (x0; y0) are the source’s coordinates. To model an outdoor environment, the sides and top of the domain were given a re ection coe cient of zero and, since Z is given as: Z = 1 +R 1 R ; (7.3) the impedance has a value of one. The discretization of these equations, and the formulation of the matrix equation implemented in MATLAB, will not be presented here, however one can  nd it in [72]. Piecewise linear shape functions were used. For a full description of the creation of the mesh and the MATLAB code, see Appendix B. 887.5. Results Figure 7.2: The anechoic chamber test con guration with the locations of receiver positions R1-R6. 7.5 Results 7.5.1 Full-Scale Laboratory Testing The results from the full-scale barrier testing in the anechoic chamber (Chapter 4) were predicted using all three prediction methods. The results in the 1000 Hz third-octave band, for the low source position at the six receiver positions shown in Figure 7.2, were predicted. Predictions were done for the no barrier case, for a re ective barrier and for an absorptive barrier. In the methods which required a di raction coe cient to be calculated | ray tracing and method of images | both the UTD and Svensson’s model were used. In FEM, di rac- tion is an inherent part of the solution to the wave equation, and therefore a di raction theory is not needed. In FEM and ray tracing, in which the boundaries of the chamber can be de ned, the walls and ceiling of the anechoic chamber were modelled as completely absorptive, with a re ection coe cient of zero or an impedance of one. In all three prediction models, 897.5. Results Figure 7.3: Measured and predicted 1000 Hz sound pressure levels with no barrier at the six receiver positions in the anechoic chamber. the painted plywood  oor was assigned a re ection coe cient of 0.9, based on spherical decoupling measurements done previously [73]. All three methods of prediction | FEM, ray tracing (PRAY) and MOI | predicted the results of the no-barrier case within 5 dB of the measured results, as shown in Figure 7.3. All accurately showed the minimum SPL at receiver position R4, however all methods underestimated the SPL at this position, with MOI and PRAY being under by 5 dB and FEM by 2 dB. All methods also overestimated the SPL at the low receiver positions, R1- R3, with FEM again giving results 2 dB from measurement and PRAY giving results 5 dB too high. Figure 7.4 shows the predicted IL’s of the barrier found using the three prediction models as well as the measured values. All prediction results had very similar overall trends to the measurement results, when comparing the variations with receiver position; however, the magnitudes of the IL’s were very di erent. FEM gave results within 2 dB to measurement at several receiver positions, however at other receiver positions results were 907.5. Results Figure 7.4: Measured and predicted 1000 Hz IL of the wall built in the anechoic chamber at receiver positions 1-6. up to 8 dB too low. The predicted IL’s using ray tracing with the UTD were up to 30 dB higher than measurement, while using Svensson’s model were up to 20 dB too high. Both di raction models performed better when implemented using the MOI, with Svensson’s model performing more accurately, giving results 2-10 dB from measurement. From these results, it was known that it was not the di raction coe cient calculations which caused the inaccurate results in ray tracing. The discrepancies between MOI and measurements may come from several things. MOI assumes that the barrier is in nitely thin, while in reality the barrier was 12 cm wide. Di raction around the edges of the barrier and second order di raction may have occurred and were not accounted for in this model. Svensson’s model proved to be more accurate in these predictions; the UTD assumes an in nitely long barrier while Svensson’s model accounts for  nite length barriers. The FEM model is a two-dimensional model and therefore does not account for any di racted sound which was not perpendicular to the barrier; this could account for the discrepancies seen between the FEM predictions and 917.5. Results measurements. Using PRAY, the high IL’s indicated a low sound level behind the barrier. This occurred because not enough rays were being di racted to reach the receivers placed behind the barrier. In ray tracing, rays are emitted in every direction; in the case of barriers outdoors there are in fact only four sound paths between a source and receiver, as discussed in regards to the MOI. Therefore, the vast majority of the rays which are emitted are unnecessary, leading to a very ine cient model. A very large amount of rays are required, leading to very long run times, and even then there are an insu cient number of rays which are di racted. In room acoustics, where ray tracing has been the most successful, there are many sound paths which allow for rays to reach a de ned receiver and each ray may have many re ections. In the case of outdoor barriers there is at most two re ections, o the ground on either side of the barrier, while most rays will not re ect at all before being absorbed by the perfectly absorbing walls and ceiling. Due to these reasons, it is hypothesized that ray tracing is not a valid method for the prediction of outdoor noise barrier performance. The MOI does not allow the barrier to be absorptive, as it is inherent in the code that the di racting edge is re ective. Therefore it was determined that FEM was the best option to perform absorption measurements. The change in IL due to absorption placed on the source side of the barrier in the anechoic chamber was investigated using FEM. Figure 7.5 shows the results, where FEM gave values within 2 dB of measurement. These discrepancies can be due to several things. The  rst is that again the predictions are done in two dimensions, ignoring all sound not perpendicular to the barrier. Another is that in the anechoic chamber, adding absorption to the front of the barrier also added 50 mm, the thickness of the ba es, to the thickness of the barrier. In the predictions, there was no increase in barrier thickness when the barrier’s source side became absorptive. 927.5. Results Figure 7.5: Measured and predicted change in IL due to absorption on the source side of the barrier, at 1000 Hz. 7.5.2 Foliage The results from Section 6.3.4, where the model foliage was characterized by comparing scale-model measurements to full-scale  eld tests, were modelled using PRAY. Receivers were placed 5 m in front of and 5 m behind the row of trees placed on grass, and the source was placed 10 m from the trees. Both the source and the receivers were 1 m above the ground, as in the measurements. A room 25 m long by 20 m wide by 6 m high was created, with perfectly absorbing ceiling and walls. Results were predicted at 125, 250, 500, 1000 and 2000 Hz. The ground re ection coe cient was determined by using the no-foliage case from the scale-model measurements and performing a best- t using the method of images. Figure 7.6 shows the measured and best- t sound pressure levels at the receiver position 5 m from the source and Table 7.1 gives the results of this  t. The foliage was modelled as a 1 m thick, 6 m high zone of volume scatterers, with a  tting density of 0.3 m 1. This value was found by comparing results with a variety of  tting densities and selecting the one which agreed best with measurement. 937.5. Results Figure 7.6: The measured and best- t predicted SPL at the receiver position 5 m from the source with no trees present, used to determine the ground re ection coe cient. Table 7.1: Grass re ection coe cients as determined by a best- t using MOI. Frequency (Hz) 125 250 500 1000 2000 Re ection Coe cient .5-.4i .4-.2i .6-.2i .3-.3i .2-.3i Figure 7.7 shows the IL due to the row of trees, both from PRAY predictions and scale-model measurements. Predictions demonstrated very similar trends to measurements. Ray tracing showed sound ampli cation of up to 1 dB in front of the barrier at several frequencies and the magnitude of the IL stayed below 1 dB, as in the measurements, until the 2000 Hz band. Using ray tracing, the IL of the foliage behind the barrier was greater in magnitude than in front, again agreeing with measurements; however the peak IL was found to be 4 dB and occurred at 500 Hz using ray tracing, as opposed to 3 dB at 1000 Hz in the measurements. These discrepancies may come from the fact that the foliage was being modelled as volume scatterers, which assumed random scattering. In reality, foliage 947.6. Summary Figure 7.7: IL of a row of trees, 5 m in front and 5 m behind the foliage. Ray tracing results (PRAY) are compared with scale-model measurements (SM). has complex absorption characteristics and do not scatter omni-directionally. Because the anechoic chamber barrier predictions showed that PRAY was an un t prediction model to use for outdoor barrier predictions, no further predictions were made on the e ects of foliage on barrier performance. FEM may be used, however tests must  rst be performed to determine how to model the foliage using  nite elements. 7.6 Summary Three prediction methods | ray tracing,  nite elements, and the method of images | were studied in hopes to show them to be useful tools in the prediction of the performance of noise barriers and the factors studied in this work. Two di raction methods were used for ray tracing and the method of images: the Uniform Theory of Di raction and Svensson’s model. Results from the full-scale anechoic chamber testing were also predicted;  nite elements and the method of images using Svensson’s model gave results closest to measurement, 957.6. Summary varying by 2-10 dB from the measured values. Some discrepancies of the MOI could be due to the assumptions of an in nitely thin barrier and no di raction around the ends of the barrier. The fact that the FEM was a two-dimensional model could account for the di erences between FEM predictions and measurements. Ray tracing using both methods of di raction gave IL results up to 30 dB higher than measurement and showed to be an inadequate modelling technique to be used for outdoor noise barriers. Since MOI does not allow for the barriers to be absorptive, the e ects of making the source side of the barrier in the anechoic chamber absorptive were predicted using the FEM. The prediction results di ered from measurement by up to 2 dB, which could be due to the fact that the thickness increase which occurred in the anechoic chamber did not occur in the model. Ray tracing was used to predict the experiments which measured the amount of sound back-scattered from and transmitted through foliage. The magnitudes of the changes in IL due to foliage were within 2 dB of measurement, with discrepancies due to the fact that the foliage was being modelled as random volume scatters. The foliage e ects on barriers were not predicted, as PRAY showed to be un t to model outdoor barrier performance. 96Chapter 8 Conclusion In this work, several factors which a ect the performance of highway noise barriers com- prising thin vertical walls were investigated with the aim of improving the practice of noise mitigation. One of these factors was making the barrier surfaces sound absorbing, which could reduce the sound ampli cation that occurs between two re ective parallel barriers. The other factor was foliage growing near a barrier; this could have both a positive or neg- ative e ect, depending on whether the foliage absorbs and back-scatters sound (decreasing noise levels) or scatters sound into the shadow zone (increasing noise levels). The main objective of this thesis was to explore these factors and determine how they a ect the performance of roadside noise barriers. This was done using four methods of investigation: full-scale barrier testing,  eld testing, scale-model testing and prediction. The  rst detailed objective was to determine the optimal amount and placement of absorption on a barrier and the e ects it has on the barrier’s performance. This was achieved by constructing a 1.2 m high barrier on a plywood  oor in an anechoic chamber. By covering the wall with di erent con gurations of absorptive material, it was determined that covering all of both sides of the wall would prevent ampli cation and give the greatest IL. The re ective wall’s IL was improved by 2-3 dBA using this con guration when the source and receiver positions were within 1.8 m of the wall and the NRC value of the absorptive material was 0.71. The distance was closer than what is typically seen in the  eld and therefore slightly lower IL improvements should be expected in practice. However the NRC value was lower than 0.8, the value recommended by the Ministry. It was seen in 97Chapter 8. Conclusion the results that an absorptive material with the highest NRC value gave the greatest IL, with an NRC improvement of 0.15 giving an IL improvement of 1-2 dBA. Prediction was to be used to achieve this objective; once the available models were validated, it was hoped that further predictions could be made of barriers with varying absorption con gurations. In order to validate three prediction models, the full-scale ane- choic chamber measurements were predicted at 1000 Hz. It was found that ray tracing gave IL results of the re ective wall which were up to 30 dB higher than measurements. From this, it was hypothesized that ray tracing is not a valid prediction method for outdoor noise barriers, due to the large amount of rays which are absorbed by the ceiling and walls with- out ever being di racted. To ensure that the errors were not due to the implementation of the di raction models, UTD and Svensson’s model were implemented into the method of images. The MOI approach was much more accurate, with Svensson’s model giving IL’s 2-10 dB from measurement and the UTD giving results 5 dB further. Svensson’s model does not assume an in nite length barrier as the UTD does, and therefore this could ac- count for the more accurate results. When using MOI one cannot make the barrier sound absorptive, as a re ective barrier is assumed. Therefore in regards to absorptive barrier predictions, this method is not relevant. FEM gave results for the re ective barrier similar to MOI using Svensson’s model, varying from measurement by 2-8 dB. This discrepancy can be due to the fact that the FEM was performed in two dimensions, and therefore sound that was not perpendicular to the barrier was ignored. However, this method appeared to be the best option in performing absorptive barrier measurements. Making the source side of the barrier sound absorptive was predicted using FEM; results were found to be within 2 dB of measurements. Discrepancies could be due to the fact that in the anechoic chamber, the e ective barrier width increased by 50 mm, the width of the ba es, while in prediction no change in width was accounted for. The second objective was to study the e ects of absorption on the performance of 98Chapter 8. Conclusion parallel barriers. A scale model was created to achieve this objective. Excess attenuation measurements, which use the  ow resistivity as a single parameter and assume the Delany- Bazley model to be valid, were performed to select the scale-model materials to model a four-lane highway. The Delany-Bazley model is valid for porous material only and was therefore not valid for hard surfaces. This could have a large impact on the performance of the scale model, and other methods of selection should be investigated. Using the scale model, more realistic source and receiver distances could be used. The source was placed in the center of the highway, 15 m from the barrier, at a height of 0.5 m. Receivers were placed 5 to 20 m behind the barriers at a height of 1.8 m. Three di erent heights of parallel barriers were used to study absorption; it was found that for parallel barriers in this con guration, adding absorption to the source side of the barriers was equivalent to increasing the re ective barriers’ height by 0.33 m. The e ects of adding either a re ective or absorptive barrier across a highway parallel to another barrier was examined. Adding a 5 m high barrier decreased the total IL of the original barrier by 1 dBA, making it less e ective. When the parallel barriers were absorptive, the IL was very similar to that of a single absorptive barrier and no ampli cation occurred. Parallel barrier predictions were not performed in this work. FEM was found to be a valid model for these predictions; however a very large mesh would be required for predictions up to 2500 Hz for barriers 30 m apart and a computer with the necessary memory was not available. The third objective was to determine the frequency-dependent e ects of nearby foliage on the performance of noise barriers. Field testing was performed at several sites to test these e ects. Time-averaged equivalent sound levels of tra c noise were taken simultane- ously behind nearby sections of barrier, one with some con guration of foliage around it and one bare. Microphones were placed 1 to 3 m behind the wall and 1.5 to 2.5 m below the top of the wall. It was found that isolating foliage e ects were di cult, as other factors 99Chapter 8. Conclusion such as the distance between the tra c and the barrier were di cult to keep constant. In the cases where conclusions could be drawn, it was seen that the height, size and density of the foliage behind the barrier had a large role. In the case of 10 m high, broad- leafed trees directly behind the barrier, a 5 dB increase in noise level was seen at frequencies above 1000 Hz, indicating scattering into the shadow zone. Below 1000 Hz the sound level decreased by up to 4 dB, indicating sound was being back-scattered or absorbed. In the case of vines growing on a barrier, which only grew 0.5 m above the barrier, up to 5 dB of sound was back-scattered and absorbed at most frequencies, and no high frequency scattering into the shadow zone was seen. Dense evergreen hedges showed a decrease in sound level by up to 5 dB at frequencies above 500 Hz, again showing that sound was back-scattered and absorbed, while less dense hedges showed e ects of less than 2 dB. The scale model was used here to test the e ects of foliage. Scale-model trees were characterized by measuring the amount of sound which propagated through them and back-scattered from them. These results were compared with  eld tests performed on an evergreen hedge. It was seen that the scale-model trees likely modelled a di erent type of foliage, as they back-scattered more and transmitted less sound than the measured hedge. It was found that foliage directly in front of or behind a barrier scattered up to 4 dB of sound into the shadow zone at high frequencies. At mid-frequencies, the foliage decreased levels behind the barrier by up to 2 dB, indicating that sound was being back-scattered or absorbed. Foliage placed 10 m behind a barrier had very little e ect on the sound level at a receiver placed directly between the barrier and the foliage. By comparing these results with the  eld tests, it was concluded that the scale-model trees more closely resembled broad-leafed trees. Predictions were also made of the scale-model foliage test which measured the amount of sound that propagated through and back-scattered from a row of trees. These predic- tions were done using ray tracing, where the foliage was modelled using volume scatterers. 100Chapter 8. Conclusion The predictions showed similar trends to measurements and were accurate within 2 dB. Discrepancies could be due to the fact that the foliage was being modelled as random vol- ume scatterers, where as in reality they do not scatter omni-directionally and have complex absorption characteristics. The e ects of foliage near barriers were not predicted, as PRAY was seen to be un t to model the performance of an outdoor barrier. The  nal objective was to determine the practical implications of this research. It was seen that a fully absorptive barrier can give an IL improvement of up to 2-3 dBA when the source and receivers are quite close to a single barrier. In the case of parallel barriers 30 m away from each other, an IL improvement due to absorption was found to be 1 dBA, which was equivalent to a re ective barrier height increase of 0.33 m. The cost bene t of this would depend on the re ective and absorptive barrier costs. However, in many cases a height increase is not possible, and if an improvement in barrier performance is necessary then making the barriers sound absorptive is a valid method, especially if the receiver is close to the tra c. It was seen that the e ects of foliage were frequency-dependent and complicated, and varied depending on the type of foliage. If a barrier is to be built near a tall, broad-leafed tree, scattering into the shadow zone should be expected above 1000 Hz, with e ects less than 8 dB. While this does not have a large impact on the total A-weighted sound level, residents may  nd high frequency noise to be more annoying. High frequency scattering was not seen with evergreen hedges; if a barrier is to be built near a dense hedge, the hedge may increase the e ectiveness of the barrier by back-scattering and absorbing sound and preventing it from reaching the shadow zone. If the hedge is not dense and the leaves are small, the e ects of the foliage should be less than 2 dB. 1018.1. Future Work 8.1 Future Work Now that this research has been performed, the practical implications can be applied in the  eld. If absorptive barriers or barriers near foliage are constructed, sound level measurements before and after construction should be studied. The selection process of scale-model materials is an area which requires further inves- tigation. Using excess attenuation measurements for model selection uses one parameter | the  ow resistivity | to choose an appropriate material. It does not account for the frequency-varying behaviour of the material. The Delany-Bazley model is assumed, which does not hold for non-porous materials. Di erent selection processes should be investigated and compared with excess attenuation measurements. There is opportunity for more work to be done when examining di erent types of foliage and their interactions with sound. There are many classi cations of foliage and an examination of the physical properties of their leaves and branches and how they interact with sound would be an interesting follow up to this work. In this work there was evidence that absorption of the leaves and branches is an important mechanism which requires further understanding. In this work, prediction was not used to study the e ects of absorption or foliage beyond predicting measurements done here. Further FEM tests can be done with a capable computer to study the e ects of di erent con gurations of absorption on both single and parallel barriers at all frequencies of interest. While PRAY can be used to study the e ects of foliage alone, it is not a valid method to predict the e ects of foliage with barriers. A further study on how to model di erent types of foliage using FEM is needed before the e ects of foliage on barrier performance can be predicted. 102Bibliography [1] British Columbia Ministry of Transportation and Highways. Revised policy for mit- igating the e ects of tra c noise from freeways and expressways. Victoria, British Columbia, November 1993. [2] K.B. Rasmussen. Outdoor sound propagation under the in uence of wind and tem- perature gradients. Journal of Sound and Vibration, 104(2):321{335, 1986. [3] V.I. Tatarskii. The E ects of the Turbulent Atmosphere on Wave Propagation. Israel Program for Scienti c Translation, Jerusalem, 1971. [4] Z. Maekawa. Noise reduction by screens. Applied Acoustics, 1:157{173, 1968. [5] T. Busch. Scale-model investigation of highway tra c noise barriers. Master’s thesis, Department of Mechanical Engineering, University of British Columbia, 1997. [6] A.D. Rawlins. Di raction of sound by a rigid screen with an absorbent edge. Journal of Sound and Vibration, 47:523{541, 1976. [7] K. Fujiwara, Y. Ando, and Z. Maekawa. Noise control by barriers - Part 2: Noise reduction by an absorptive barrier. Applied Acoustics, 10(3):167{179, 1977. [8] T. Isei. Absorptive noise barriers on  nite impedance ground. J. Acoust. Soc. Jpn., 1:3{10, 1980. [9] D.N. May and M.M. Osman. Highway noise barriers: New shapes. Journal of Sound and Vibration, 71(1):73{101, 1980. 103Bibliography [10] W. Bowlby, L.F. Cohn, and R.A. Harris. A review of studies of insertion loss degrada- tion for parallel highway noise barriers. Noise Control Engineering Journal, 28(2):40{ 54, 1987. [11] D.C. Tobutt and P.M. Nelson. A model to calculate tra c noise levels from complex highway cross-sections. Transport Research Laboratory Report RR 245, Crowthorne, UK, 1990. [12] K. Fujiwara, D.C. Hothersall, and C. Kim. Noise barriers with reactive surfaces. Applied Acoustics, 53:255{272, 1998. [13] P.A. Morgan, D.C. Hothersall, and S.N. Chandler-Wilde. In uence of shape and absorbing surface - A numerical study of railway noise barriers. Journal of Sound and Vibration, 217(3):405{417, 1998. [14] G.R. Watts and N.S. Godfrey. E ects on roadside noise levels of sound absorptive materials in noise barriers. Applied Acoustics, 58:385{402, 1999. [15] A. L’Esperance, J. Nicolas, and G.A. Daigle. Insertion loss of absorbent barriers on ground. J. Acoust. Soc. Am., 86:1060{1064, 1989. [16] N. Ilgurel and M.S. Sozen. Comparison of the plain-shape noise barrier’s e ectiveness with and without absorptive layer by means of measurements in the semi-anechoic chamber. Euronoise, 2009. [17] C.F. Eyring. Jungle acoustics. J. Acoust. Soc. Am., 18(2):257{270, 1946. [18] F.M. Wiener and D.N. Keast. Experimental study of the propagation of sound over ground. J. Acoust. Soc. Am., 31(6):724{733, 1959. [19] T.F.W. Embleton. Sound propagation in homogeneous deciduous and evergreen woods. J. Acoust. Soc. Am., 35(8):1119{1125, 1963. 104Bibliography [20] D. Aylor. Noise reduction by vegetation and ground. J. Acoust. Soc. Am., 51(1B):197{ 205, 1972. [21] E.S. Morton. Ecological sources of selection on avian sounds. The American Naturalist, 109:17{34, 1975. [22] D.I. Cook and D.F. Van Haverbeke. Trees and shrubs for noise abatement. University of Nebraska College of Agricultural Experimental Station Bulletin, RB246, 1993. [23] J. Kragh. Pilot study on railway noise attenuation by belts of trees. Journal of Sound and Vibration, 66(3):407{415, 1979. [24] D. Aylor. Sound transmission through vegetation in relation to leaf width. J. Acoust. Soc. Am., 51(1B):411{414, 1972. [25] M.A. Price, K. Attenborough, and N.W. Heap. Sound attenuation through trees: Measurements and models. J. Acoust. Soc. Am., 84(5):1836{1844, 1988. [26] M.J.M. Martens. Foliage as a low-pass  lter: Experiments with model forests in an anechoic chamber. J. Acoust. Soc. Am., 67(1):66{72, 1980. [27] R.M. Hoover. Tree zones as barriers for the control of noise due to aircraft operations. Bolt, Beranek and Newman Inc., Report 844, 1961. [28] D.I. Cook and D.F. Van Haverbeke. Suburban noise control with plant materials and solid barriers. In: Heisler, Gordon M.; Herrington, Lee P., eds. Proceedings of the con- ference on metropolitan physical environment; Gen. Tech. Rep. NE-25. Upper Darby, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station, pages 234{241, 1977. [29] T. Van Renterghem, D. Botteldooren, W.M. Cornelis, and D. Gabriels. Reducing 105Bibliography screen-induced refraction of noise barriers in wind by vegetative screens. Acta Acustica united with Acustica, 88:231{238, 2002. [30] T. Van Renterghem and D. Botteldooren. E ect of a row of trees behind noise barriers in wind. Acta Acustica united with Acustica, 88:869{878, 2002. [31] L. De Geetere. Analysis and improvement of the experimental techniques to assess the acoustical re ection properties of boundary surfaces. PhD thesis, Katholieke Univer- siteit Leuven, 2004. [32] ISO/CD 10534-2. Determination of sound absorption coe cient and impedance in impedance tubes - Part 2: Transfer-function method. 2004. [33] H. Boden and M. Abom. In uence of errors on the two-microphone method for mea- suring acoustic properties in ducts. J. Acoust. Soc. Am., 79:541{549, 1986. [34] C. Bibby. Point-source design and performance. Technical report, University of British Columbia, 2009. [35] V.F. Spandock. Akustische modellversuche. Annalen der Physik, 20:345{360, 1934. [36] M.E. Delany, A.J. Rennie, and K.M. Collins. Scale model investigations of tra c noise propagation. National Physics Laboratory, Report Ac 58, Sept. 1972. [37] D.A. Hutchins, H.W. Jones, and L.T. Russell. Model studies of acoustic propagation over  nite impedance ground. Acustica, 52(3):169{178, 1983. [38] D.A. Hutchins, H.W. Jones, and L.T. Russell. Model studies of barrier performance in the presence of ground surfaces. Part I - Thin, perfectly re ecting barriers. J. Acoust. Soc. Am., 75(6):1807{1816, 1984. 106Bibliography [39] K.V. Horoshenkov, D.C. Hothersall, and K. Attenborough. Porous materials for scale model experiments in outdoor sound propagation. Journal of Sound and Vibration, 194(5):685{708, 1996. [40] D.A. Hutchins, H.W. Jones, B. Paterson, and L.T. Russell. Studies of parallel barrier performance by acoustical modelling. J. Acoust. Soc. Am., 77(2):536{546, 1985. [41] R. Pirinchieva. Model study of the sound propagation behind barriers of  nite length. J. Acoust. Soc. Am., 87(5):2109{2113, 1990. [42] M.M. Osman. MTC Scale model facility for transportation noise problems: Materials choice and validation for scale modelling. Technical report 77-AC-4, Ontario Ministry of Transportation and Communications, June 1977. [43] C.W. Menge. Highway noise: Sloped barriers as an alternative to absorptive barriers. Noise Control Engineering, 14(2):74{78, 1980. [44] D.C. Hothersall, D.B. Horoshenkov, P.A. Morgan, and M.J. Swift. Scale modelling of railway noise barriers. Journal of Sound and Vibration, 243(2):207{223, 2000. [45] M.E. Delany and E.N. Bazley. Acoustical properties of  brous absorbent materials. Applied Acoustics, 25(114):339{344, 1971. [46] H.E. Bass, L.C. Sutherland, and A.J. Zuckerwar. Atmospheric absorption of sound: Update. J. Acoust. Soc. Am., 88(4):2019{2021, 1990. [47] ANSI S1.26-1978. American national standard method for the calculation of the absorption of sound by the atmosphere. American National Standards Institute, 1978. [48] H.E. Bass, L.C. Sutherland, A.J. Zuckerwar, D.T. Blackstock, and D.M. Hester. At- mospheric absorption of sound: further developments. J. Acoust. Soc. Am., 97(1):680{ 683, 1995. 107Bibliography [49] F. Matta and A. Reichel. Uniform computation of the error function and other related functions. Mathematics of Computation, 25(114):339{344, 1971. [50] C.F. Chien and W.W. Soroka. Sound propagation along an impedance plane. Journal of Sound and Vibration, 43(1):9{20, 1975. [51] C.F. Chien and W.W. Soroka. A note on the calculation of sound propagation along an impedance surface. Journal of Sound and Vibration, 69(2):340{343, 1980. [52] R.K. Pirinchieva. Model study of sound propagation over ground of  nite impedance. J. Acoust. Soc. Am., 90(5):2678{2682, 1991. [53] R.K. Pirinchieva. Erratum: Model study of sound propagation over ground of  - nite impedance [J. Acoust. Soc. Am. 90, 2678-2682 (1991)]. J. Acoust. Soc. Am., 94(3):1722, 1993. [54] M.R. Stinson. A note on the use of an approximate formula to predict sound  elds above an impedance plane due to a point source. J. Acoust. Soc. Am., 98(3):1810{ 1812, 1995. [55] J. Novak. Technical note: Sound source for scale model measurements of tra c noise. Applied Acoustics, 24(1):63{70, 1988. [56] T.A. Busch and M.R. Hodgson. Improved method for selecting scale factors and model materials for scale modelling of outdoor sound propagation. Journal of Sound and Vibration, 243(1):173{181, 2001. [57] T.F.W. Embleton, J.E. Piercy, and G.A. Daigle. E ective  ow resistivity of ground surfaces determined by acoustical measurements. J. Acoust. Soc. Am., 74(4):1239{ 1244, 1983. 108Bibliography [58] J.B. Keller. Geometrical theory of di raction. Journal of the Optical Society of Amer- ica, 52(2):116{130, 1962. [59] R.G. Kouyoumjian and P.H. Pathak. A uniform geometrical theory of di raction for an edge in a perfectly conducting surface. Proceedings of the IEEE, 62(11):1448{1461, 1974. [60] T. Kawai. Sound di raction by a many-sided barrier or pillar. Journal of Sound and Vibration, 79(2):229{242, 1981. [61] N. Tsingos, T. Funkhouser, A. Ngan, and I. Carlbom. Modeling acoustics in virtual environments using the uniform theory of di raction. Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pages 545{552, 2001. [62] M.A. Biot and I. Tolstoy. Formulation of wave propagation in in nite media by normal coordinates with an application to di raction. J. Acoust. Soc. Am., 29(3):381{391, 1957. [63] H. Medwin. Shadowing by  nite noise barriers. J. Acoust. Soc. Am., 64(4):1060{1064, 1981. [64] U.P. Svensson, R.I. Fred, and J. Vanderkooy. An analytic secondary source model of edge di raction impulse responses. J. Acoust. Soc. Am., 106(5):2331{2344, 1999. [65] U.P. Svensson and P.T. Calamia. Edge-di raction impulse responses near specular- zone and shadow-zone boundaries. Acta Acustica united with Acustica, 92:501{512, 2006. [66] U.P. Svensson, P.T. Calamia, and S. Nakanishi. Frequency-domain edge di raction for  nite and in nite edges. Acta Acustica united with Acustica, 95:568{572, 2009. 109[67] M. Hodgson, O. Cousins, G. Chan, and V. Valeau. Ray-tracing prediction of sound- pressure and sound-intensity  elds in empty and  tted rooms. J. Acoust. Soc. Am., 123(5):3760, 2008. [68] A.M. Ondet and J.L. Barbry. Modeling of sound propagation in  tted workshops using ray tracing. J. Acoust. Soc. Am., 85(2):787{796, 1989. [69] G. Chan. Prediction of low-frequency sound-pressure  elds in  tted rooms for active noise control. Master’s thesis, Department of Mechanical Engineering, University of British Columbia, 2005. [70] B. Yousefzadeh. Acoustical modeling of the transient response of rooms using a beam- tracing model. Master’s thesis, Department of Mechanical Engineering, University of British Columbia, 2010. [71] J.B. Allen and D.A. Berkley. Image method of e ciently simulating small-room acous- tics. J. Acoust. Soc. Am., 65(4):943{950, 1979. [72] S.C. Brenner and L.R. Scott. The Mathematical Theory of Finite Element Methods. Springer, 2008. [73] S. Daltrop. Measurement of the acoustical characteristics of surfaces using the spher- ical decoupling method. Technical report, University of British Columbia, 2010. 110Appendix A Di raction Theory A.1 Uniform Theory of Di raction Figure A.1: A di racting edge, with de nitions of the parameters used in the UTD formu- lation. [61] The UTD assumes an in nitely long, perfectly re ecting wedge. The sound di racted by an edge Pd can be de ned in terms of parameters de ned in Figure A.1 and the incident sound Pi as: Pd = Pi D(n; k;  ; r;  i;  i;  d) A(r;  ) e  ikr: (A.1)  i is the angle between the incident direction and the vector lying along the edge. A is an attenuation term dependent on the distances from the edge to the source and receiver: A(r;  ) = r r r +  : (A.2) 111A.1. Uniform Theory of Di raction D is the di raction coe cient which accounts for the amplitude and phase change due to the di racting edge: D(n; k;  ; r;  i;  i;  d) =  e i =4 2n p 2k sin  i cot   + ( d   i) 2n  F  kLa+( d   i)  + cot    ( d   i) 2n  F  kLa ( d   i)  + cot   + ( d +  i) 2n  F  kLa+( d +  i)  + cot    ( d +  i) 2n  F  kLa ( d +  i)   ; (A.3) where F (x) is a Fresnel integral, given by: F (X) = 2i p XeiX Z 1 p X e i 2 d : (A.4) L is a distance parameter, given as: L = r r +  sin2  i (A.5) and a is de ned as: a ( ) = 2 cos2  2 N n  2  ; (A.6) where N are the integers that satisfy the following relations the closest: 2 N n  =   : (A.7) 112A.2. Svensson’s Model Kawai [60] gives a rational approximation for F (X): F (X) = 8 >>>< >>>: p  X  1 p X 0:7 p X+1:2  ei  4 q X X+1:4 for X < 0.8  1 0:8(X+1:25)2  ei  4 q X X+1:4 for X  0.8 (A.8) Approximations are also used for N : N+ = 8 >>>< >>>: 0 for    (n 1) 1 for  >  (n 1) ; N = 8 >>>>>>>< >>>>>>>:  1 for  <  (1 n) 0 for  (1 n)     (1 + n) 1 for  >  (1 + n) (A.9) A.2 Svensson’s Model Figure A.2: The di racting edge, with de nitions of the parameters used in the Svensson model. [65] The Svensson model uses a line integral formulation along a  nite-length di racting edge to model the edge as a secondary source when hit by a sound wave. Much of this derivation is taken from references [65] and [66], and a cylindrical coordinate system 113A.2. Svensson’s Model with the axis along the di racting edge is used. Assuming an ei!t time dependence, the frequency-domain edge-di raction transfer function is given by: Hdiffr(!) =   4 4X j=1 Z z2 z1 e ik(m+l)  j ml dz (A.10) where  =  = W is the wedge index and z1 and z2 are the two ends of the edge. m and l are the distances between the edge and the source S and receiver R, respectively, given by: m = q r2S + (z  zS) 2; l = q r2R + (z  zR) 2: (A.11) The  j’s are edge-source directivity functions, given by:  j = sin(  j) cosh(  ) cos(  j) (A.12) where the angles  j are:  1 =  +  S +  R;  2 =  +  S   R  3 =    S +  R;  4 =    S   R: (A.13) The auxiliary function  is:  = cosh 1  ml + (z  zS)(z  zR) rSrR  : (A.14) Figure A.3 shows the three di erent zones around an edge for a given source position. Neglecting di raction, a receiver in Zone 1, say R1, will receive direct and specularly re ected sound. A receiver in Zone 2, such as R3, will receive only direct sound. A receiver in Zone 3, say R5, will receive neither, and is therefore called the shadow zone. When di raction occurs, di racted sound reaches all three zones. For receivers lying on 114A.2. Svensson’s Model Figure A.3: The zones around a di racting edge. [65] the boundaries, say R2 and R4,  R =    S and a singularity occurs for a certain value of z in Equation A.10. This value is called the apex point, the point which gives the shortest source-edge-receiver path length and is denoted za, given by: za = zRrS + zSrR rS + rR : (A.15) If za is not contained within the limits of integration z1 and z2, the singularity has no e ect and regular numerical-integration techniques can be used. For ease of notation, the parameter zrel = z  za is used, and therefore the bounds of integration are z01 = z1  za and z02 = z2 za. In order to integrate e ciently, the integration range is split up into three parts: a small region around the apex point where zrel = 0, which contains the singularity, and from each limit of integration to that region. Using zsplit to denote a point on the di raction edge very close to the apex point, Equation A.10 can be rewritten as the sum 115A.2. Svensson’s Model of three di erent terms: Hdiffr(!) =I1 + I2 + I3 =  2  4 4X j=1 Z zsplit 0 e ik(m+l)  j ml dzrel   4 4X j=1 Z  zsplit z01 e ik(m+l)  j ml dzrel   4 4X j=1 Z z02 zsplit e ik(m+l)  j ml dzrel: (A.16) I2 and I3 have no singularities and can be solved using ordinary numerical-integration; in this work the MATLAB function quadgk was used with a relative tolerance of 10 6, as suggested by Svensson et al. [66]. The  rst term includes a singularity, and an approxi- mation of the integrand must be used. Since the range of integration is very close to the apex point, the  rst term can be rewritten as: I1 =  2  4 e ik(m0+l0) 4X j=1 Z zsplit 0  j ml dzrel (A.17) where m0 and l0 are the distances from the apex point to the source and receiver, respec- tively. For this to be valid, it is necessary for zsplit to satisfy the following conditions: zsplit << s 2m0l0(m0 + l0) k(rS + rR)2 zsplit <<m0; zsplit << l0: (A.18) The following approximations were used for the integrand: cosh(  )  1 +  2 (1 +  )4 2 2R20 z2rel (A.19) 116A.2. Svensson’s Model ml  R20 (1 +  )2 + cos R0(  1)  + 1 zrel + sin2  (1 +  2) 2 z2rel  cos 2  z2rel (A.20) where R0 = m0 + l0 and  is the horizontal angle between the ray and the edge:  = sin 1  rS + rR R0  : (A.21) 117Appendix B Creation of Finite Element Mesh The  nite element code was implemented in MATLAB. For the creation of the mesh, the PDE toolbox and the command pdepoly were used . The toolbox was opened and the boundary locations were de ned by the command ‘pdepoly([0 0 3.6 3.6],[0 2.6 2.6 0])’, which labeled the domain as P1. The barrier was de ned using the command ‘pdepoly([1.74 1.74 1.86 1.86],[0 1.2 1.2 0])’ and labeled P2. To create the mesh for the no barrier case, the mesh was initialized on P1 only. The mesh was then re ned four times and the coordinate, boundary and element matrices were exported into MATLAB. To create a mesh for the barrier case, a mesh was initialized on the domain P1-P2, which left the barrier out of the domain. Again, this was re ned four times before the matrices were exported to MATLAB. Once the matrices p, e and t are de ned, the following MATLAB script was run, using the function assemble as de ned below. f=900:50:1100; k=2*pi*f/343; P2L=zeros(length(f),6); for mm=1:length(f) [Ah,fh]=assemble(p,e,t,k(mm)); uh=Ah\fh; R=zeros(1,6);cL=zeros(1,6); for n=1:length(p) % find elements within receiver radius if p(2,n)-.2 < .1 if ((p(1,n)-2.4)^2+(p(2,n)-.2)^2)<1E-3 R(1)=R(1)+uh(n); cL(1)=cL(1)+1; elseif ((p(1,n)-3)^2+(p(2,n)-.2)^2)<1E-3 R(2)=R(2)+uh(n); cL(2)=cL(2)+1; 118Appendix B. Creation of Finite Element Mesh elseif ((p(1,n)-3.6)^2+(p(2,n)-.2)^2)<1E-3 R(3)=R(3)+uh(n); cL(3)=cL(3)+1; end end end for n=1:length(p) if p(2,n)-1.05 < .1 if ((p(1,n)-3.6)^2+(p(2,n)-1.05)^2)<15E-3 R(4)=R(4)+uh(n); cL(4)=cL(4)+1; elseif ((p(1,n)-3)^2+(p(2,n)-1.05)^2)<1E-3 R(5)=R(5)+uh(n); cL(5)=cL(5)+1; elseif ((p(1,n)-2.4)^2+(p(2,n)-1.05)^2)<1E-3 R(6)=R(6)+uh(n); cL(6)=cL(6)+1; end end end P2L(mm,:)=P2L(mm,:)+R./cL; end P_tot=20*log10(abs(P2L)/2E-5); P=zeros(1,6); for ii=1:length(f) P=P+10.^(P_tot(ii,:)/10); end SPL=10*log10(P)-10*log10(length(f)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [Ah,fh]=assemble(coords,boundary,elems,k) Nnod=length(coords); % number of nodes Nedge=length(boundary); % number of boundary edges Nel =length(elems); % number of elements fh=zeros(Nnod,1); % allocate load vector Ah=sparse(Nnod,Nnod); % allocate stiffness matrix for n=1:Nel % loop over elements x0=coords(1,elems(1,n)); % coordinates of the vertices y0=coords(2,elems(1,n)); % of triangle n x1=coords(1,elems(2,n)); y1=coords(2,elems(2,n)); x2=coords(1,elems(3,n)); 119Appendix B. Creation of Finite Element Mesh y2=coords(2,elems(3,n)); mx=1/3*(x0+x1+x2); % barycenter my=1/3*(y0+y1+y2); det=(x1-x0)*(y2-y0)-(x2-x0)*(y1-y0); % determinant of mapping area=0.5*det; % area of triangle D=[y1-y2, y2-y0, y0-y1; x2-x1, x0-x2, x1-x0]; AK=0.25/area*transpose(D)*D; % element stiffness matrix MK=area/12*[2 1 1; 1 2 1; 1 1 2]; % element mass matrix if ((mx-0.8)^2+(my-0.25)^2)<0.01 value=-50; % within source radius else value=0; % not within source radius end FK=area*value*[1/3;1/3;1/3]; % element load vector for kk=1:3 % loop over shape functions iii=elems(kk,n); % global index of shape function iii for l=1:3 % inner loop over shape functions j=elems(l,n); % global index of shape function l Ah(iii,j)=Ah(iii,j)+AK(kk,l)-k^2*MK(kk,l); % update global matrix end fh(iii)=fh(iii)+FK(kk); % update load vector end end for ii=1:Nedge % loop over edges in boundary x1=coords(1,boundary(1,ii)); % coordinates of the vertices y1=coords(2,boundary(1,ii)); x2=coords(1,boundary(2,ii)); % coordinates of the vertices y2=coords(2,boundary(2,ii)); h=max(abs(x1-x2),abs(y1-y2)); B=h/6*[2 1; 1 2]; if (abs(x1)==0 && abs(x2)==0) || (abs(x1)==3.6 && abs(x2)==3.6) || (y1==2.6 && y2==2.6) B=i*k*B; % absorbing wall elseif y1==0 && y2==0 B=i*k*B/19; % ground, z=19 (R=0.9) else B=i*k*B/9; % barrier, R=0.8 end Ah(boundary(1,ii),boundary(1,ii))=Ah(boundary(1,ii),boundary(1,ii))+B(1,1); Ah(boundary(2,ii),boundary(2,ii))=Ah(boundary(2,ii),boundary(2,ii))+B(2,2); Ah(boundary(2,ii),boundary(1,ii))=Ah(boundary(2,ii),boundary(1,ii))+B(2,1); Ah(boundary(1,ii),boundary(2,ii))=Ah(boundary(1,ii),boundary(2,ii))+B(1,2); end 120

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Country Views Downloads
China 41 110
Hong Kong 13 0
United States 11 1
Republic of Korea 4 0
Canada 4 0
Australia 3 1
India 3 0
Philippines 2 1
Russia 2 0
Indonesia 2 0
France 2 0
United Kingdom 2 0
Japan 2 0
City Views Downloads
Beijing 23 0
Unknown 22 4
Chengdu 12 4
Central District 8 0
Shenzhen 5 3
Ashburn 5 0
Jakarta 2 0
Montreal 2 0
Tokyo 2 0
Cologne 1 0
Los Angeles 1 0
Saint Petersburg 1 0
Redmond 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0072221/manifest

Comment

Related Items