Single frequency sound propagation in flat waveguides with locally reactive impedance boundaries

A coherent image source method is presented for evaluating single frequency sound propagation from a point source in a flat waveguide with two infinite and parallel locally reactive boundaries. The method starts from formulating reflections of the spherical sound radiation into integrals of plane wave expansion, and the analytical evaluation of the integrals is simplified by introducing a physically plausible assumption that wave front shapes remain the same before and after each reflection on a reflective boundary. The proposed model can determine coherently the sound fields at arbitrary receiver locations in a flat waveguide, even when one boundary is highly sound absorptive. Being compared with the classical wave theory and the existing coherent ray-based methods, it is shown that the proposed method provides considerable accuracy and advantages to predict sound propagation in flat waveguides with a sound absorptive ceiling and a reflective floor over a broad frequency range, particularly at large distances from the source where the existing methods are problematic.