Reverberation in waveguides with rough surfaces

An impedance formalism for treating scattering at multiple rough boundaries in waveguides with depth-varying sound speeds is developed. The formalism is used to give a compact result for the time history of multiply scattered reverberant sound. In general, the multiple scattering contribution to reverbation decays more slowly than the single scattering contribution. When attenuation mechanisms other than surface scattering are small, the reverberant field has a diffusive character, and this leads to algebraic (∼1/t) decay of the reverberation of originally pulsed signals. As a by-product of the formalism, conventional reverberation models are derived from “first principles.” The derivation provides the precise form of the scattering strength used in such models. In addition, it shows that the mean field should be used for propagation to and from the scattering surface. Finally, the computations present the possibility of treating the scattering by two rough boundaries simultaneously.