Reflection of a Plane Acoustic Wave from a Surface of Nonuniform Impedance

Abstract

A theoretical analysis is made of the reflection of a plane wave of sound from a surface whose acoustic impedance is not uniform. The sound pressure received at a distant point consists of a specularly reflected wave plus scattered radiation. The magnitude of the specularly reflected wave is independent of wavelength and depends upon the impedance of the portion of the surface which may be viewed at the specular angle from the receiver. If the impedance differs only slightly from a constant value the directivity pattern of the scattered radiation is determined by the product of three factors. The condition for the scattered radiation to obey Lambert's cosine law is that the reflecting surface is one of approximately zero pressure and that there is no correlation in the impedance irregularities. The condition for perfectly diffuse scattered radiation is that the surface behave as approximately rigid with no correlation in the impedance irregularities. In the case of a surface whose impedance irregularities have a slow statistical variation with position the scattered radiation is confined to a beam whose axis lies along the direction of specular reflection but the energy within the beam is not necessarily closely confined to the specular angle.