On the three-dimensional sound fields from a moving monopole source above a non-locally reacting ground

This study derives an accurate analytic solution for sound fields due to a moving point monopole source above a non-locally reacting ground. Based on the property of the invariant phase function, the acoustic pressure and normal particle velocity are matched across the air/ground interface in the frequency-wave number domain. Expressions for the integral form of the sound fields in three different frames are used to analyze and compare the original physical frame in the reception time geometry, the Lorentz frame, and the emission time frame. For ease of interpretation, the final form of the asymptotic solution is expressed in the geometry of the emission time frame. The accuracy of the asymptotic solution is validated using the direct numerical integration technique. The three-dimensional point source solution derived from the current study is compared with that of the two-dimensional line source solution. Explicit comparisons of the cylindrical and spherical wave reflection coefficients are available, allowing a better understanding of the impact of the ground wave term in the vicinity of a non-locally reflecting plane. Finally, contour plots are presented that demonstrate the need to employ the asymptotic formula for the non-locally reacting ground instead of approximating it with a locally reacting property.