A Mathematical Analysis Concerning the Edge Effect of Sound Absorbing Materials

In this paper we present a contribution to the explanation of the experimentally observed fact that the sound absorption coefficient of sound absorbing materials as measured in the reverberation chamber depends on the dimensions of the test sample. The cause of this effect can be attributed to the sound diffraction phenomena in the vicinity of the edges of the sample which result in an additional sound absorption. In a rough approximation this additional absorption increases linearly with the edgelength of the sample without showing any dependence on the geometry of the sample. This is a good simplification but this fails when the sample becomes too small. It indicates that there is a lower limit to the sample size for which the additional absorption is a true edge effect. It is the purpose of this paper to throw some light upon the effect of the geometry upon the edge effect. For this reason we investigate the edge effect for a sound absorbing strip, lying in an infinitely large, rigid plane.

In a zeroth-order approximation the strip is considered as being a superposition of two opposite sound absorbing half-planes. The diffraction of a plane wave by such a device is determined with the aid of the Wiener-Hopf technique. This mathematical model agrees with the general idea that the edge effect is a local effect in the vicinity of the edge. A mathematical refinement can be obtained by assuming that some interaction between the local edge fields occurs. It turns out that the interaction term in the total diffracted field is of the order (k d)^−3/2 where d is the stripwidth. Some numerical calculations concerning the influence of the interaction term upon the extinction cross-section of the strip will be given.