Application to radiative acoustics of Whitham's method for the analysis of non-equilibrium wave phenomena

Abstract

An approximate method due originally to Whitham is applied to the study of acoustic waves propagating in a non-grey radiating and absorbing gas, assumed in local molecular equilibrium. The method, which has general applicability in the study of non-equilibrium wave phenomena, replaces the exact governing equation by a set of lower-order equations that can be solved analytically in many cases. The use of the method is demonstrated by reconsidering the onedimensional problems of (i) harmonic waves driven by a harmonic variation in either position or temperature of a planar wall and (ii) the discrete wave produced by the impulsive motion of a constant-temperature wall. The method greatly simplifies the mathematics for these problems, and comparaison of the results with those of earlier investigators shows the approximate method to be accurate. Moreover, the method allows us to obtain a more systematic and complete analytical solution of the second problem than has been obtained by more conventional methods.