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1916]          ON  THE  ATTENUATION  OF  SOUND  IN THE  ATMOSPHERE             421
plane form. The wave train cannot then be propagated forward without further change, but it may be regarded as being composed of a plane wave train of smaller amplitude, together with waves which are dispersed in all directions, and are due to the effect of the turbulence of the original train. If d is the diameter of an eddy, \ is the wave length of the sound, U is the velocity of the air due to the eddy, and V is the velocity of sound, the amount of sound energy dispersed from unit volumes of the main wave is
where E is the energy of the sound per unit volume. If the turbulence is uniformly distributed roimd the source of sound then, as Lord Rayleigh points out, the sound energy will be uniformly distributed because the energy dispersed from one part of the wave front will be replaced by energy dispersed from other parts ; but if the turbulence is a maximum in any particular direction then more sound energy will be dispersed from the wave fronts as they proceed in that direction than will be received from the less turbulent regions. Regions of maximum turbulence should, therefore, be regions of minimum sound. The turbulence is usually a maximum near the ground. The intensity of sound should, therefore, fall off near the ground at a greater rate than the inverse square law, even although there is no solid obstacle between the source of sound and the listener.]now concerned. The problem of the grating is trea Theory of Sound, 2nd edition,  272 a.