Acoustic scattering by a parallel pair of semi-infinite wave-bearing surfaces

Two wave-bearing surfaces, which might be either membranes or thin elastic plates, occupy the regions x > 0, y = 0 and x > 0, y = d in a Cartesian coo rdinate system. They are connected to a supporting structure at x < 0, 0 < y < d: the surfaces at z < 0, y = 0 or y = d are taken to be acoustically h ard and the end face at z = 0, O < y < d is either acoustically soft or har d. The system is irradiated by an incident plane wave of velocity potential Re{exp(ikx cos theta + iky sin theta - i omega t)}. The problem is formula ted as a pair of integrodifferential equations for the unknown transverse v elocities Re{V(x) exp(-i omega t)} and Re{W(x) exp(-i omega t)} of the vibr ating surfaces. A Wiener-Hopf analysis reduces the problem to that of an in finite system of algebraic equations for coefficients that are related to t he unknown normal velocity (or potential) across the end face x = 0, 0 < y < d. Numerical results compare well with independently obtained asymptotic solutions for the limit when the fluid loading and plate separation distanc e are small.