Acoustic eigenfrequencies in concentric spheroidal-spherical cavities

The acoustic eigenfrequencies f(nsm) in concentric spheroidal-spherical cavities are determined for both Dirichlet and Neumann boundary conditions. Two types of cavities are examined, one with spheroidal outer and spherical inner boundary and inversely for the other. The pressure field is expressed in terms of both spherical and spheroidal wave functions, connected with one another by well-known expansion formulas. When the solution is specialized to small values of h = d/(2R(2)) where d is the interfocal distance of the spheroidal boundary and R-2 the half length of its rotation axis, exact closed-form expressions are obtained for the coefficients g(nsm)((2)), and g(nsm)((4)) in the resulting relations f(nsm)(h) = f(ns) (0) [1 + g(nsm)((2)) h(2) + g(nsm)((4)), h(4) + O(h(6))]. Numerical results are given for various values of the parameters. (C) 1997 Academic Press Limited.