The penetration of sound into an extended reaction ground due to an arbitrarily oriented dipole.

Abstract

An asymptotic solution is derived for the sound fields below an extended reaction ground due to an arbitrarily oriented dipole placed near the air/ground interface. The derived approximate solutions are compared with accurate numerical schemes based on the fast field formulation and the direct numerical integration of the Fourier integral. It has been shown that the sound field above the ground can be computed accurately by using the concept of effective impedance [K. M. Li et al., J. Acoust. Soc. Am. 104, 679–685 (1998)]. The effective impedance approach is used to derive the asymptotic formula for predicting the penetration of sound into the extended reaction ground. However, there are apparent discrepancies in the predicted sound fields according to the analytical solution and the accurate numerical schemes. A modified analytical formula is then developed that leads to more accurate numerical results. The resulting analytical formula due to an airborne acoustic excitation may be used as a basis for a future study to compute the particle displacements induced by an elastic object buried in a rigid‐frame porous medium.