Acoustic radiation from a spherical source embedded eccentrically within a fluid sphere

Abstract

The radiation from a spherical source vibrating with an arbitrary, axisymmetric, time-harmonic velocity distribution while positioned at an arbitrary point within a fluid sphere, which is embedded in another infinite fluid medium, is computed. This configuration is an idealization of a spherical acoustic lens, with focal point inside the lens, when used as a sound projector. The translational addition theorem for spherical wave functions is used to express series of wave modes centered at one sphere in terms of modes centered at the other, thereby facilitating the task of satisfying the boundary conditions. The radiation load on the source and the farfield directivity pattern are evaluated for representative values of the many parameters that characterize the problem, such as the wavelength size of the lens and source, the relative characteristic impedances and sound velocities of the two fluid media, the position of the source, and the velocity distribution on the source sphere. In general, no great increase in the radiation resistance is noted when the source is at the focal point of the lens. The focal points for monopole and dipole sources are usually not coincident. The size of the source has little effect upon the farfield directivity pattern.