Scattering near a penetrable finite plane

Abstract

Acoustic scattering due to a point source by a penetrable finite plane introducing the Kutta-Joukowski condition is studied. This investigation is important in the sense that point source is regarded as fundamental radiating device. Mathematical problem which is solved is an approximate model for a noise barrier which is not perfectly rigid and therefore transmits sound. Approximate boundary condition depends upon the thickness and material constants which constitute the finite plane. The problem is solved using integral transforms, the Wiener-Hopf technique and asymptotic methods. It is found that the diffracted field is sum of the fields produced by the two edges of the finite plane and an interaction field. It is once again found that the field produced by the Kutta-Joukowski condition will be substantially larger than the field produced in its absence when the source is near the edge. Finally, physical interpretation of the result is discussed.