Scattering by an Array of Cylinders as a Function of Surface Impedance

Plane waves are considered impinging at normal incidence on a half-space (or slab of considerable thickness) containing a random array of cylinders. The average attenuation per unit distance within the array is evaluated numerically for various sizes of scatterers, radius a = 0.1–10 cm, concentrations 10−5−3×10−3 cm−2, and surface impedance from 0 to ∝. It is found that attenuation is exactly proportional to radius and approximately proportional to concentration over these ranges of parameters. As a function of stiffness reactance and ka (k being the wavenumber of the incident sound field), the attenuation becomes infinite at the origin of the ka, X/ρc plane, but is otherwise zero when ka = 0; elsewhere, the function is a series of ridges radiating from the vicinity of the origin these ridges are sharp and high close to the origin, becoming broader and lower further away; each ridge is curved, being convex to the ka axis. For any given value of stiffness reactance, X/ρc, the greatest attenuation is found at frequencies near the value given by ka = X/ρc. When X/ρc is a mass reactance, no interesting features arise and the surface is a gently sloping plateau.