DIFFRACTION OF AN ACOUSTIC PLANE-WAVE BY A RECTANGULAR PLATE

A scalar field diffracted by a rigid rectangular plate can be computed with the formula that Otsuki derived by applying the properties of We ber-Schafheitlin's discontinuous integral (also referred to as the Kob ayashi potential). This method may be regarded as giving an eigenfunct ion expansion of the wave functions of the present configuration, alth ough these functions are expressed by double infinite integrals. Expan sion coefficients are determined from the matrix equations, and the ma trix elements are given by double infinite integrals. An algorithm eff ective for computing these integrals is developed here by using the as ymptotic expansions for the integrands. As a result, the original inte gral reduces to a finite double integral plus two finite single integr als. The numerical results for some diffraction patterns are presented . With relatively large plates, the results agree well with those obta ined from the Kirchhoff diffraction integral. (C) 1997 American Instit ute of Physics.