On the asymptotic solution of sound penetration into a rigid porous half-plane: A modified saddle point method

An approximate analytical formula has been derived for the prediction of sound penetration into a semi-infinite rigid porous medium due to a monopole source. The sound fields can be expressed in an integral form that is amenable to analytical and numerical analyses. A modified saddle point method is applied to evaluate the integral asymptotically, which leads to a closed-form expression. The validity of the asymptotic formula is confirmed by comparison with the numerical results computed by the fast field formulation and the direct evaluation of the integral. The present analytical formula has been demonstrated to be sufficiently accurate to predict the penetration of sound into the semi-infinite rigid porous medium.