Propagation of sound from a monopole source above an impedance-backed porous layer.

In this article, the propagation of sound from a monopole source above an impedance-backed porous layer is examined. The sound fields can be expressed in an integral form that is amenable to further analysis. A standard method of steepest descents is applied to evaluate the integral where the method of pole subtraction is needed to obtain a uniform asymptotic solution for the sound field above the plane surface. To obtain a numerical solution, the location of the pole was determined numerically by means of the Newton-Raphson method. Based on the pole location, the sound fields can then be calculated numerically. It has been demonstrated that the use of a plane wave reflection coefficient to calculate the sound fields is a special case of the asymptotic formula when the pole is located further away from the saddle point.