Scattering of Plane Compressional Waves by a Spherical Obstacle

The scattering of plane compressional waves by a spherical obstacle in an elastic solid, which was investigated by Ying and Truell is examined further. For a rigid inclusion, the boundary conditions are redefined to take into consideration the motion of the inclusion inside the solid. By a proper limiting process, it is shown that the solutions for a rigid insert, a fluid sphere, a cavity, or an obstacle in a fluid are all derivable from the general results of an elastic inclusion. The rates of energy scattering due to a small rigid obstacle (a«λ) are found to be inversely proportional to the fourth power of wavelength.