The link between the plane-wave absorption coefficient and the sound field due to a point source

The knowledge of the sound field is important in many studies of acoustics. The more boundary conditions are correct the more the results are close to real values. Usually boundary conditions are expressed in terms of the surface acoustic impedance Z_s that in general depends on porous material properties such as its airflow resistivity, thickness or bending stiffness. The simpler way to model a porous material is to give a constant value of the surface acoustic impedance Z_s (f) for a given frequency on the porous material surface. However, for extended reaction materials, if a plane wave impinges on the porous material surface with different incidence angle ϑ_i, the surface acoustic impedance Z_s (f,ϑ_i ) is also affects by the latter parameter. In real situations, any plane wave exists and the sound field is more complicated therefore it is interesting to understand the real/practical applicability of this theory. In other words, if a designer should choose a porous material to control the sound field he usually considers “plane-wave” ignoring the behavior of the material in a much more complex sound field. Considering a spherical wave is, of course, a subsequent approximation, however, by studying the sound field due to a point source over a porous material in free space it is possible to find a link between the simple plane-wave theory and what really happens to the sound field.