Numerical Approach to Far Field Acoustic Wave Propagation from a Prolate Spheroidal Surface

A method is described for calculating the far field, transient, three-dimensional pressure field generated by acoustic waves emanating from a prolate spheroidal surface. The pressure field is expanded in a series of spherical harmonics, which leads to a system of linear, tridiagonal, one dimensional wave equations that can be integrated efficiently by numerical techniques based on the method of characteristics. Integrals involving orthogonal functions are approximated by a numerically robust scheme where exact orthogonality is obtained (in the absence of round-off errors) in terms of weighted sums over a discrete variable.