ABSTRACT
As in wave problems for acoustic layer (Chapter 3), the problem considered here demon› strates the power of the Fourier transform.
Let a plane acoustic wave fall from below, propagating in direction of vertical axis y in the Cartesian coordinate system (x, y): pinc(x, y) = eiky . The problem is thus considered as two›dimensional. We will study here integral equations arising in diffraction by an acoustically hard linear obstacle placed over the axis x, i.e., somewhere at y = 0. If the obstacle occupies the whole axisx: y= 0, –∞<x<∞, then the problem is one›dimensional, and is reduced to a simple ordinary differential equation with constant coefcients. If there is a nite›length obstacle, then we consider simultaneously the two problems genetically related to each other:
α) There is a rigid screen placed on |x| ≤ a, y = 0. β) There is a gap (hole) in the innite hard screen, occupying the interval |x| ≤ a, y = 0.
In H¤onl et al. (1961) you can nd some general results, which establish a relationship between these two problems.
