The influence of wind and temperature gradients on sound propagation, calculated with the two-way wave equation

Abstract

A method is introduced to calculate the influence of wind and temperature gradients in stratified media on sound propagating above an absorbing ground surface. It is based on the ‘‘two-way wave equation’’ for the Fourier transforms of the sound pressure P and its derivative V. The vector containing P and V is stepwise extrapolated through the medium in the direction perpendicular to the ground surface, fulfilling the boundary conditions at the ground surface, at a top level, and at the source height. The propagation equations for P and V appear as simple plane-wave equations, and computer (CPU) time within each layer is very low. Therefore, many thin layers (in the order of centimeters if desired) can be applied, and any complicated gradient can be used. Calculations for a homogeneous atmosphere, with a computer program based on this model, show an excellent agreement with previous models. When a wind profile is present, results are mainly compared with measurements by Parkin and Scholes [P. H. Parkin and W. E. Scholes, J. Sound Vib. 1, 1–13 (1964); 2, 353–374 (1964)]. They show very good agreement in the no-wind and downwind cases. In the upwind situation, agreement is very good below 500 Hz. Above this value the model does not predict sound to penetrate into the shadow region, while Parkin and Scholes found (low) sound levels.