Acoustic scattering from a sphere with nonuniform surface impedance

A general mathematical method is presented for computing effective overpressure distribution in the near and far field regions around a sphere with uniform or nonuniform surface acoustic impedance distribution in the presence of a plane acoustic wave, first for impedance distributions which are symmetric about the axis of approach of the incoming plane wave, then for nonsymmetric distributions with proofs of convergence of the solution method being presented for both symmetric and nonsymmetric cases. Numerical examples are computed and presented graphically for rigid spheres, infinitely soft spheres, spheres with uniform finite surface impedance, and spheres with several types of nonuniform impedance distribution. It is concluded that any model designed to reproduce diffraction patterns of the human head should have a partial covering of material with finite surface impedance to account for the effects of the hair on the effective overpressure distribution. (Modified author abstract)