The Spherical Wave Functions

Abstract

All acoustic radiation problems can be boiled down to solving the wave equation subject to certain initial and boundary conditions. For a constant frequency case, the problem reduces to solving the Helmholtz equation [40], ${\nabla}^2\widehat{p}+{k}^2\widehat{p}=0$, subject to certain boundary conditions on the source surface. This sounds simple but in reality the analytic solution to the Helmholtz equation exists only for certain types of source geometry that the Helmholtz equation is separable. In most engineering applications the source geometry is arbitrary, so the analytic solution to the Helmholtz equation cannot be found. In these circumstances numerical or approximate solutions are sought.