We apply the methods developed in our preceding paper (J. A. Imbeau and B. T. Darling. Can. J. Phys. 57, 190(1979)) for calculating the Green's function of a cavity to obtain the normal modes and normal frequencies of the cavity. As the frequency of the driving point source approaches that of a normal frequency the response (Green's function) of the cavity becomes infinite, and the form of the Green's function is dominated by the normal mode. There is also a 180° reversal of phase in passing through a resonance. In this way, we are able to calculate the normal frequencies of prolate spheroidal cavities to the full precision employed in the calculations (16 significant digits for double precision of the IBM-370). The Green's functions and the normal functions are also obtainable to a high degree of precision, except in the immediate vicinity of the surface of the cavity where they suffer a well-known discontinuity.
Green’s function and image system for the Laplace operator in the prolate spheroidal geometry
