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UBC Theses and Dissertations

The fundamental mathematical and acoustical properties of woodwind and brass instruments Krush, Joseph Martin

Abstract

The contents of this thesis belongs entirely to the area of instrumental acoustics. It is written in the style of a textbook for music students, and aims to serve an instructional and informative purpose. The first goal of the paper is to outline the manner in which woodwind and brass instruments function. Similarities and differences between individual instruments and families of instruments are discussed. The basis of the thesis is a disclosure of the physical properties of sound waves in general, waves in cylindrical tubes, waves in conical tubes, and waves in both these types of tubes with certain boundary conditions imposed on them. These properties are directly applied to the woodwind instruments, but they cannot be applied to brass instruments; consequently, a different procedure is adopted for their discussion. The original goal of the author was to discuss the most salient known, proven mathematical and acoustical properties of woodwind and brass instruments. In the process of doing this, conclusions evolved which led to a claim and subsequent formation of theories which are, to the best of the writer's knowledge, presented here for the first time, and which still remain to be completely proven by complex mathematical methods.

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