The Accuracy of Doubly Asymptotic Approximations for an Acoustic Half-Space

The accuracy of doubly asymptotic approximations (DAAs) for acoustic half-space problems is assessed by examining their performance for a canonical problem in bispherical coordinates. Exact specific acoustic impedance curves for axisymmetric modal vibrations of a spherical surface near a planar boundary are generated, and corresponding curves based on the first-order DAA and the curvature-corrected DAA are compared with their exact counterparts. The comparisons show that the curvature-corrected DAA is substantially more accurate than the first-order DAA. Also, the curvature-corrected DAA is found to be satisfactory for broad-band excitations regardless of the sphere’s proximity to a compliant (zero-pressure) surface; for a rigid surface, the approximation is satisfactory only if the sphere is located at least one diameter away from the boundary.