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SOUND TRAVELING-WAVES IN WIND INSTRUMENTS AS SOLUTIONS TO NON LINEAR NON HOMOGENEOUS GAS DYNAMICS EQUATIONS

By Alain-yves Leroux

Abstract

Abstract. The sound propagation is usually described by a linear homogeneous wave equation, though the air flow in a duct is described by the gas dynamics equations, using a variable cross section, which corresponds to a non linear non homogneous system. The aim of this paper is to exhibit a common periodic solution to both models, with several free parameters such as frequency or amplitude, able to represent any sound. By taking in account a friction term linked to the material (wood or brass for instance) of the duct, it is possible to build an analytic such solution when the cross section fullfills some condition which corresponds exactly to the general shape of the wind instruments. The conclusion is that in the wind intruments, the shape yields linearity

Topics: S(q, m(q
Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.410.5990
Provided by: CiteSeerX
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