REFLECTION AND TRANSMISSION OF SCALAR WAVES BY A PERIODIC ARRAY OF SCREENS

An exact solution has been obtained for scattering of a plane scalar wave by a periodic array of screens. By taking advantage of the geometrical periodicity, the problem statement has been reduced to a singular integral equation for an unknown field discontinuity over a single screen. The singular integral equation has been solved by expanding the unknown quantity in Chebyshev polynomials and solving the coefficients from a set of algebraic equations. The scattered field consists of a superposition of wave modes, each with its own cut-off-frequency. A reflection coefficient has been defined in terms of the coefficient of the zeroth-order scattered wave. This coefficient has been computed as a function of the frequency for various geometrical configurations. The exact results have been compared with three approximations.