Scattering of Plane Waves by a Rigid Sphere in an Acoustic Quarterspace

The acoustic scattering by a submerged spherical rigid obstacle near an acoustically hard concave corner, which is insonified by plane waves at arbitrary angles of incidence, is studied. The formulation utilizes the appropriate wave-harmonic field expansions and the classical method of images in combination with the translational addition theorems for spherical wave functions to develop a closed-form solution in form of infinite series. The analytical results are illustrated by numerical examples where the spherical object is located near the rigid boundary of a fluid-filled quarterspace and is insonified by plane waves at oblique angles of incidence. Subsequently, the basic acoustic field quantities such as the form function amplitude, the scattered far-field pressure, and the scattered acoustic intensity are evaluated for representative values of the parameters characterizing the system. The limiting case involving a spherical object submerged in an acoustic halfspace is considered and good agreement with a well-known solution is established.