The penetrable coated sphere embedded in a point source excitation field

A low frequency acoustic wave field emanates from a given point and fills u p the whole space. A penetrable lossy sphere with a coeccentric spherical c ore, which is also penetrable and lossy but characterized by different phys ical parameters, disturbs the given point source field. We obtain zeroth- a nd first-order low frequency solutions of this scattering problem in the in terior of the spherical core, within the spherical shell, and in the exteri or medium of propagation. We also derive the leading nonvanishing terms of the normalized scattering amplitude, the scattering cross-section as well a s the absorption cross-section. The special case of a penetrable sphere is recovered either by equating the physical parameters that characterize the media in the shell and in the exterior, or by reducing the radius of the co re sphere to zero. By letting the compressional viscosity of the medium in the interior sphere, or in the shell, go to zero, we obtain corresponding r esults for the lossless case. The incident point source field is so modifie d as to be able to obtain the corresponding results for plane wave incidenc e in the limit as the source point approaches infinity. It is observed that a small scatterer interacts stronger with a point source generated field t han with a plane wave. A detailed analysis of the influence that the geomet rical and the physical parameters of the problem have on the scattering pro cess is also included. An interesting conclusion is that if the point sourc e is located at a distance more than five radii of the scatterer away from it, then no significant changes with the plane excitation case are observed . (C) 2000 Elsevier Science B.V. All rights reserved.