Acoustic diffraction by a finite number of small soft bodies

The scattering problem of an incident plane sound wave by a finite number of small soft-sound arbitrarily shaped bodies is considered. A system of first-class Fredholm integral equations is posed which, for the small bodies, yields a system of potential equation sequences for power solution expansion. Reciprocity relations were exploited to construct the first and second order asymptotic models which give approximate solutions valid for a large number of small bodies. The leading two terms of the asymptotics for the farfield amplitude and the scattering cross section are obtained. The case of a several elliptic discs is considered in detail.