The eigenfrequencies of spheroids obtained from an integral phase matching condition

Abstract

The complex acoustic eigenfrequencies of impenetrable spheroids have been found previously by satisfying the boundary conditions with spheroidal wavefunctions [$. M. D'Archangelo et al., J. Acoust. Soc. Am. 77, 6 (1985)]; alternately, they are obtained here by using a T‐matrix code. However, a physical explanation of the eigenfrequencies can be given in terms of surface waves circumnavigating the spheroid along a geodesic, and a phase matching condition can be written down which takes the form of an integral, due to the variations of the surface wave propagation constant along the path. A model is used in which the propagation constant is approximated by the known one on a sphere, with the same local radius of curvature along the propagation direction. This condition serves either to obtain the complex eigenfrequencies, or to test the accuracy of eigenfrequencies obtained by other methods. [Supported by NSRDC and ONR.]