Sound Fields Generated by a Monopole Point Source Moving above a Locally Reacting Surface

The sound field generated by a harmonic monopole noise source traveling at a constant speed above an impedance ground surface has been derived using the method of steepest descent. A Doppler shift, which represents the instantaneous wavefront experienced at particular point on the ground surface due to source motion, is applied to modify the frequency dependent ground impedance. The Doppler factor varies continuously as the source moves past a ground-based receiver. An asymptotic solution similar to the classical Weyl-Van der Pol formula for grazing incidence is proposed and validated against the results obtained by the Fast Field Program (FFP) formulation. Due to the asymmetry of the problem, a two-dimensional sound field is desired at each plane of constant elevation. The computationally intensive two-dimensional algorithm, which has order of N2, can be applied directly to model the full wave equation. However, this FFP algorithm becomes computationally expensive when the source is located at high elevations operating at high frequencies. As an alternative, a radial slice approximation can be applied to reduce the computational demands to order N, while achieving similar results. A more efficient solution obtained via asymptotic analysis has been used to validate the FFP schemes.