The attenuation of sound by a randomly irregular impedance layer

Abstract

This paper examines the scattering of sound which occurs at the irregular boundaries of a nominally uniform, two dimensional impedance layer. At sufficiently high frequencies classical Kirchoff diffraction theory can be applied to obtain two coupled integral equations which describe the acoustic properties of the impedance layer. These equations are derived, and an expression for the attenuation of sound by the layer is obtained by means of a method which avoids the awkward renormalization argument commonly invoked when scattering integrals are approximated for large distances by the method of stationary phase and the scattering body itself extends to infinity. The theory is applied to the case of the transmission of sound through a randomly irregular impedance layer of helium in air. This is an important problem in the study of jet noise suppression and has been examined experimentally by Norum (1973). Norum discovered that the shielding properties of a low Mach number, two dimensional helium jet are markedly different from those predicted by the simple theory which models the jet as a plane, parallel sided impedance layer. Numerical results are presented, and it is argued that the scattering mechanism discussed in this paper substantially accounts for the experimental attenuation patterns.