Propagation of sound in the vicinity of rigid porous interfaces

Propagation of sound in the vicinity of rigid porous interfaces is investigated systematically to facilitate the acoustical characterization of sound absorption materials for noise reduction applications. Various rigid porous interfaces are considered: (1) a semi-infinite porous layer; (2) a porous hard-backed surface; and (3) a porous impedance-backed layer. A closed-form solution and numerical methods are derived with respect to each rigid porous interface condition. A modified saddle-point method is exploited to investigate the sound field emanating from a monopole source above and below a rigid porous interface. The solutions can be expressed in a form that resembles the classical Weyl-Van der Pol formula. A heuristic method is then proposed to remove the singularity within the asymptotic solution via application of the double saddle-point method. Its relative simplicity and accuracy demonstrates the advantage of the double saddle-point method whenever the approximation is valid. Following this, the sound field within a hard-backed rigid porous medium due to an airborne source is examined. The accuracy of the proposed asymptotic solutions has been confirmed by comparison with benchmark numerical solutions and through indoor sound propagation experiments. Measurement data and theoretical predictions suggest that when the receiver is positioned near the top surface of the hard-backed layer, the ground reflection of the refracted wave contributes greatly to the total sound field. Taking into account source characteristics, an asymptotic formula is derived for predicting the sound field from a dipole source above and below an extended reaction ground. The directional effect of the dipole source on each term within the asymptotic solutions is interpreted. Further analysis shows that an accurate asymptotic solution can provide a good starter field for the Parabolic Equation--Finite Element Method (PE/FEM). The PE/FEM marching schemes are derived based on linear and cubic finite element discretization along both the vertical and horizontal directions. The Perfectly Matched Layer (PML) technique is applied to the PE/FEM, resulting in a substantial reduction in computational time. Comparison with experimental data for snow covered grounds is made and good agreement was demonstrated, which validates the accuracy of the proposed PE/FEM approach