Integral method for modeling the sound field above a porous material

A new concept of a transmission technique for the characterization of porous material is presented. It is based on the accurate modeling of the sound field above the layer of material that rests on an horizontal infinite baffle. The sound field is generated by a waveguide mounted vertically under the baffle with its termination flush to the baffle. The waveguide is assumed to create a uniform distribution of particle velocity at the termination. The field in the material is expressed using a Green’s function that accounts for the multiple reflections on the baffle and at the upper surface of the material. The field above the material is formulated in terms of the pressure gradient distribution over the upper surface. Starting with the boundary conditions at the upper surface (continuity of the sound pressure and normal particle velocity), the collocation method is used to solve for the pressure gradient at a mesh on this surface. This, in turn, allows one to calculate the sound pressure above the material and the transfer function between the volume velocity of the source and this sound pressure. Numerical results are presented, and the potential of this technique for the characterization of porous material is discussed.