Propagation of Sound in Inhomogeneous Media: Exact, Transient Solutions in Curvilinear Geometries

Abstract

Exact solutions for one-dimensional, transient acoustic wave propagation in curvilinear geometries with mean temperature variations are presented in this paper. These solutions are obtained by using a transformation of the spatial and acoustic variables in a manner suggested by the WKB approximation. The analysis is performed for spherical and cylindrical co-ordinate systems. Temperature profiles admitting exact traveling wave type solutions are derived. Although these solutions resemble the approximate, “high frequency,” WKB form of solution of the wave equation, they have the interesting property that they are exact, regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity. Calculations showing the propagation of waves in cylindrical and spherical geometries are presented.