Multipole Expansion of Sound Radiation from Moving Rigid Bodies

Abstract

The solution of the wave equation with a source term extended in space and moving as a rigid body with translation and rotation is expanded about an interior point in terms of point multipoles, which are expressed as spatial derivatives of the Lienard-Wiechert solution for a monopole. An application to sound radiation from moving rigid bodies is given using the theory of Ffowcs-Williams and Hawkings [Phil. Trans. Roy. Soc. London A264, 321 (1969)]. As examples, the radiation fields of a rotating ellipsoid and a sphere in accelerated rectilinear motion are estimated.