Natural frequencies of circular disks

The natural frequencies or the singularity expansion method (SEM) poles are computed for circular disks. We treat the acoustically soft disk, i.e, the Dirichlet boundary condition, and the perfectly conducting disk. The poles are found by an application of the -matrix method by searching the zeros of a determinant. The poles associated with the first values of the azimuthal index are shown in both cases, and numerical values are given in tables and figures. The internal resonances are also computed for the thin oblate spheroidal cavity and comparisons are made with the thin circular cylindrical cavity.