Diffusion of waves in a layer with a rough interface
Sound trapped between the rough boundaries of a statistically homogeneous layer can exhibit diffusive behavior which influences the reverberation of a pulsed signal. If the interfaces of the layer can transmit sound, then eventually sound within the layer will be lost and there will be no diffusion. Nevertheless, if the transmission to the exterior of the layer is weak, there will be a remnant of diffusion. This paper examines the description of this kind of quasidiffusive behavior for sound which impinges on the rough interface of such a layer from outside the layer. As in the case of diffuse light scattering by particles in suspension, the diffusion constant is renormalized according to the delay required to build up resonant energy in the layer. In addition, when there is a density contrast between the interior and exterior of the layer, or when there is dispersion, the diffusion constant has another correction associated with energy flux within the layer.