Wave Motion 32 (2000) 319–338 The penetrable coated sphere embedded in a point source excitation field George Dassios ∗,a , Maria Hadjinicolaou b , Gregory Kamvyssas a a Department of Chemical Engineering, School of Engineering, University of Patras and ICEHT/FORTH, GR-26500 Patras, Greece b Department of Environmental and Natural Resources Management, University of Ioannina at Agrinio, GR-30100 Agrinio, Greece Received 5 March 1999; received in revised form 2 February 2000 Abstract A low frequency acoustic wave field emanates from a given point and fills up the whole space. A penetrable lossy sphere with a coeccentric spherical core, which is also penetrable and lossy but characterized by different physical parameters, disturbs the given point source field. We obtain zeroth- and first-order low frequency solutions of this scattering problem in the interior of the spherical core, within the spherical shell, and in the exterior medium of propagation. We also derive the leading nonvanishing terms of the normalized scattering amplitude, the scattering cross-section as well as 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 core 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 results for the lossless case. The incident point source field is so modified as to be able to obtain the corresponding results for plane wave incidence in the limit as the source point approaches infinity. It is observed that a small scatterer interacts stronger with a point source generated field than with a plane wave. A detailed analysis of the influence that the geometrical and the physical parameters of the problem have on the scattering process is also included. An interesting conclusion is that if the point source 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. © 2000 Elsevier Science B.V. All rights reserved. 1. Introduction The theory of scattering has been developed for an arbitrary incident field, both in the frequency and in the time domain [20]. Nevertheless, exact analytic solutions for simple objects are obtained, almost always, in the frequency domain and for a plane incident wave. This is so, since the plane wave, which has its singularity at infinity, enjoys a periodic transverse homogeneity, perpendicular to the direction of propagation, which somehow maximizes the simplicity of the incident field. The situation becomes extremely simple, when the scatterer exhibits some kind of spherical symmetry, because of the well-known expansion formula that expresses any spectral Fourier component in terms of spherical waves centered at the origin [26,27]. Consequently, the excitation field is adjusted to the geometry of the scatterer, and then linearity and orthogonality allow for the component by component evaluation of the solution. ∗ Corresponding author. E-mail address: dassios@iceht.forth.gr (G. Dassios) 0165-2125/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII:S0165-2125(00)00042-1