THE RADIATION FORCE ON A SPHERICAL OBSTACLE IN A CYLINDRICAL SOUND FIELD

Abstract

The corresponding problems of the radiation forces acting on a spherical obstacle in a plane or spherical progressive sound field have been examined previously by King (Proc. Roy. Soc. (London), A, 147:212.1934) and Embleton (J. Acoust. Soc. Amer. 26:40. 1954) respectively. In these cases the sound field and scattering obstacle both have symmetry of revolution about the line joining the center of the obstacle to the origin of the sound field, but for a cylindrical sound field there exists only a much lower degree of symmetry. A general expression has been obtained for the radiation force in terms of the complex amplitudes of spherical harmonics required to synthesize the incident sound field—for the cases of greatest symmetry this reduces to the simpler expression previously obtained. The first 20 non-zero amplitudes have been evaluated for a cylindrical sound field and it is shown that the force is one of attraction near to the source, becomes zero at a certain distance, and is a force of repulsion at a greater distance. Qualitatively, this force is the same as for spherical waves but for any size of obstacle and frequency of the sound field the point of zero force is always nearer to the source in a cylindrical wave.