  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.
