Acoustic diffraction by a thin soft torus

The scattering problem of an incident plane sound wave with a fixed wave number by a thin soft-sound torus with arbitrary shaped cross-section is considered. The method of matched asymptotic expansions is used to construct a formal asymptotic solution of the problem. The asymptotic model, which is described by a well-posed integral equation, is constructed with the help of a modified matching procedure. The leading terms of the asymptotics for the farfield amplitude and the scattering cross-section are obtained. The case of a circular torus with constant cross-section is considered in detail. The constructed asymptotic solution is valid at low and medium frequencies where the acoustic wavelength ranges, as compared with the characteristic size of the obstacle, from a very much large value down to one comparable with its size.