Sound travellingwaves in wind instruments as solutions to non linear homogeneous gas dynamics equations
Langue
en
Document de travail - Pré-publication
Résumé en anglais
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 ...Lire la suite >
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 brings the linearity.< Réduire
Mots clés en anglais
waves
acoustics
gas dynamics
linear appearance
Origine
Importé de halUnités de recherche