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Graph Modelling of Musical Wind Instruments: A Method for Natural Frequencies Computation

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Many aspects of the musical wind instruments behavior can be studied within the framework of 1D acoustic propagation. A common method is based on an analogy with electric transmission lines, in which the impedance is a central concept. The present work proposes a diff erent approach, based on results from mathematical modelling and analysis of repetitive structures such as networks of strings or beams. The method, that keeps at the one dimensional level, uses concepts and methods from graph theory for modelling the duct of wind instruments. A key point is a special matrix reformulation of the original wave equation on a graph. The focus is on natural frequencies computations for complex, piecewise cylindrical ducts. Examples with or without toneholes illustrate the method and its potential through symbolic computations. In the case of closed-open piecewise cylindrical resonators, the approach answers in a practical way a conjecture formulated twenty years ago by Dalmont and Kergomard, which is then replaced in the general framework of inverse spectral problems. An assertion of Benade is checked on one woodwind example.
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Document Type: Research Article

Publication date: November 1, 2015

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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