Low frequency diffraction by a hard strip

The problem of solving the reduced wave equation with the normal derivative of the solution given on a strip leads to an integro-differential equation. In this paper we show how a rigorous solution of this integro-differential equation can be obtained when the product of strip width and wave number is small. As an application of the method of solution we study the problem of diffraction of a plane wave. We are thus able to verify some earlier results obtained in a formal manner and show that these results do indeed represent the first few terms of a convergent expansion.