Ultrasonic scattering by a rigid sphere in the nearfield of a circular piston

Abstract

This paper presents a new method for calculating the velocity potential Ø of scattered ultrasonic waves from a rigid sphere placed freely in the nearfield of a circular piston in an infinite baffle. The solution Ø is given in the form of an infinite series of spherical surface harmonics as a function of reduced quantities ka, kr₀, kR, kr, etc., where k is the wavenumber, a is the radius of the sphere, r₀ is the distance from the piston to the center of the sphere, and R is the radius of the piston. The theoretical framework has the advantages that it includes neither approximations nor numerical integrations, and that it is applicable to elastic or compressible sphere cases with slight modifications of the boundary conditions.