Acoustic diffraction by two concentric coaxial soft spherical caps

Summary The subject of this paper is the problem of diffraction of a time-harmonic axially symmetric acoustic wave by two concentric coaxial soft spherical caps. An integral equation technique is employed to solve such a boundary value problem involving two concentric coaxial spherical caps. Approximate expressions are derived for the far field amplitude as well as the scattering cross section for this problem when the incident wave is a low frequency axially symmetric plane wave travelling along the common axis of the two caps. By taking appropriate limits, the formulae for scattering cross section for the corresponding problems for a soft spherical cap, a soft sphere and a soft sphere bounded by a concentric soft spherical cap are also derived. Furthermore, the total electrostatic charge required to raise the two concentric coaxial spherical caps to unit potentials in a free space is readily evaluated from the analysis of this paper.