The Residual Variable Method Applied to Acoustic Wave Propagation from a Spherical Surface

Abstract

The classical wave equation in spherical coordinates is expressed in terms of a residual potential applying the Residual Variable Method. This method essentially eliminates the second derivative of the potential with respect to the radial coordinate from the wave equation. Thus, the dynamic pressure distribution on the surface of a spherical cavity can be studied by considering the cavity surface only. Moreover, the Residual Variable Method, being amenable to “marching” solutions in a finite-difference implementation, is very suitable for the analysis of acoustic wave propagation into the finite medium from the cavity surface. The propagation of the wave from the internal surface can be followed numerically. There is no need to discretize the infinite domain in its entirety at all. The propagation analysis can be terminated at any point in the radial direction without having to consider the rest.