Acoustic Waves in an Inhomogeneous Medium

Abstract

Until now, we have only considered the scattering of acoustic and electromagnetic time-harmonic waves in a homogeneous medium in the exterior of an impenetrable obstacle. For the remaining chapters of this book, we shall be considering the scattering of acoustic and electromagnetic waves by an inhomogeneous medium of compact support, and in this chapter we shall consider the direct scattering problem for acoustic waves. We shall content ourselves with the simplest case when the velocity potential has no discontinuities across the boundary of the inhomogeneous medium and shall again use the method of integral equations to investigate the direct scattering problem. However, since boundary conditions are absent, we shall make use of volume potentials instead of surface potentials as in the previous chapters.