Acoustic scattering by a cluster of small sound-soft obstacles

The scattering problem of an incident plane sound wave by a finite number of small sound-soft arbitrarily shaped obstacles is considered. First, we study the case of multiple scattering in the long wave limit. By analogy with Greenwood's approximation for the electrical constriction resistance of a circular cluster of microcontacts, we obtain an approximation for the harmonic capacity of a system of a large number of small sound-soft obstacles grouped into a spherical cluster. We generalize Greenwood's approach for the case of an arbitrary convex cluster and, as a by-product of our analysis, we elicit an approximate formula for the harmonic capacity of a convex solid. The study of the general case of multiple scattering by a cluster of small soft-sound obstacles is based on the first order asymptotic model obtained in our previous paper. We use the method of artificial small parameter for constructing Padé approximants of the scattering amplitude. Explicit formulas are derived and illustrated on several examples.