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It is assumed that the equation of the sea surface is z = ζ(xyt), and that the time average Φ = 〈ζ(x′y′t)ζ(x″y″t)〉 is a function only of ξ = x″ − x′, η = y″ − y′. The scattering coefficient of long-wave sound is calculated and shown to be σ = (c2k2/4π)2∫∫Φ(ξη) exp−ik(aξ+bη)dξdη, where 2π/k is the wavelength of the sound, and a, b, c are, respectively, the sum of the x, y, z direction cosines of the incident and scattered rays. For short-wave sound, the formula is more complicated, but independent of the wavelength of the sound, as it should be. However, it is shown that experiments with short waves yield much less information about the sea surface than do those with long waves. This is unfortunate, since the latter experiments are much more difficult than the former.
Carl Eckart (Fri,) studied this question.