On the Non-Specular Reflection of Sound from Absorbent Surfaces

Abstract

The non-specular reflection of plane waves of sound by certain surfaces composed of either absorbing semicylindrical or hemispherical bosses on an infinite plane has been analyzed. Solutions in terms of eigenfunctions for the problem of the single boss (with arbitrary impedance Z) on an infinite plane (of impedance Z′ = ∞, 0) and a plane wave at an arbitrary angle of incidence have been derived through consideration of a cylinder or sphere and two simultaneously incident “image waves.” The asymptotic solutions (Kr≫1) were then extended to consider certain finite (of maximum extent≪r) patterned distributions and both finite and infinite uniform random distributions of small bosses (Ka < 1), subject to the restriction that only the primary excitation be considered. (The analogous distributions of whole cylinders and spheres were also treated.) The results obtained for the various cases were then compared in the plane of incidence.