On the sound field from a source moving above non-locally reacting grounds

Abstract

This paper investigates the sound fields generated by a source moving horizontally at a constant speed above a non-locally reacting flat ground. The present study offers an extension of an earlier study that focused on sound fields owing to a moving source above a locally reacting ground. However, a locally reacting ground model may not be sufficient for many acoustic “soft” grounds such as snow-covered ground or a layer of sound-absorbing materials. An integral representation for the sound fields is obtained by means of a Lorentz transform. Further analysis using the steepest descent method is then applied and leads to a uniform asymptotic approximation for the total sound fields. The explicit connection between the Lorentz frame and the physical space is explored. This allows for a closed-form analytical expression written in the emission time frame for arbitrary spatial locations of a moving source and stationary receiver. The asymptotic solution is validated by comparing it with a direct numerical solution of the time-domain linearized Euler equations. The analytical solution, which is referred to as the Dopplerized Weyl-van der Pol (D-WVDP) formula, generalizes the earlier theoretical results to allow for the source motion and non-locally reacting ground surfaces. An approximation scheme can further be identified, and its range of validity is discussed.