The problem which Lord Rayleigh considered (reflection from a corrugated surface) and which several have treated approximately in recent years, is developed in a general form. An exact solution is obtained by extensive use of Wiener's generalized harmonic analysis. This solution is readily extended to include electromagnetic waves, general elastic waves, and nonplanar, nonharmonic sources. Numerical evaluation of the formulas is considered by means of an operational representation, from which various types of successive approximations can be constructed. Applications can be of special interest in scatter communications and in underwater sound transmission and reverberation. Experimental evidence from the latter area indicates that a rather detailed theory is necessary for an adequate account of the situation.