Reflection and Transmission of Sound From a Dipole Source Near a Rigid Porous Medium

An asymptotic analysis has been conducted to examine the sound fields due to an arbitrarily oriented dipole that is placed above a rigid porous medium. In the study, the diffraction of sound owing to the effect of spherical wavefronts and the presence of the porous interface has been explored. By using a double saddle point analysis supplemented by the pole subtraction method, the asymptotic solutions for the dipole sound fields reflected from and transmitted through the porous interface have been derived. The diffracted wave contributions in both situations can be expressed conveniently in terms of a standard complementary error function that can be computed efficiently. By using these asymptotic formulas, the total sound fields in the vicinity of a rigid porous medium can be calculated accurately and rapidly.