Propagation of sound waves in a moving medium

Abstract

The propagation of sound waves radiated by a two-dimensional source in a fluid moving with subsonic velocity between two perfectly reflecting parallel walls is considered. The steady state problem appears to have a non-unique solution, for which Sommerfeld's radiation condition does not apply. Two methods are used for obtaining the unique solution. First the corresponding problem for a fluid with non-zero bulk viscosity is solved, which has a unique solution and then the limit for zero bulk viscosity is taken. Secondly, the initial value problem for a source being switched on at timet=0 is solved and it is shown that its solution tends to the same steady state solution in the limit fort → ∞. In the last section the results for the corresponding axisymmetric case are given. In the appendix some properties of the twodimensional steady state solution are explained qualitatively.