Theories of rough surface reflection by Rayleigh, Eckart, and Brekhovskikh are utilized to calculate the dependence, on surface and radiation parameters, of the amplitudes of reflected radiation when an acoustic beam is incident on a pressure-release surface with sinusoidal corrugations. The results of these theories are compared, with emphasis on the assumptions used. Experimental results for the reflection of an underwater acoustic beam from this type of surface are presented and compared with each of the theories. The best agreement between theory and experiment is obtained for surfaces of small slope, indicating that this criterion is basic to the validity of the theories. However, surprisingly similar results are obtained for surfaces of large slope. The theories seem to predict the behavior of the lower orders of reflection more closely than that of the higher orders. Good agreement between theory and experiment is obtained for directions of reflection and for cut-off frequencies.
When a series of uniform acoustic pulses is transmitted through a medium whose refractive index varies in a r~ndom manner, the received pulses vary randomly about an average amplitude. A theory developed by Mmtzer D. Acoust. Soc. Am. 25, 922 (1953) ] predicts that the coefficient of variation V, defined as the fractional standard deviation of a series of pulses, is directly proportional to k (271-/acoustic wavelength), provided that the range from the source to receiver is greater than ka 2 , where a is the correlation distance of the refractive index variations. In a scaled model experiment the refractive index variations are caused by heating the medium (water) from below, thus causing turbulent convection. Observations show the linear dependence of V upon frequency for r>ka 2 as predicted by the theory. At the higher frequencies, observations indicate possible oscillations in V as it tends toward a frequency independent value.
The Rayleigh solution for reflection from a corrugated surface, and some possible modifications, are examined. For small slopes these methods produce similar analytical expressions and almost identical numerical results. When the first nonradiating term is included in the computations, the magnitude of the scattered amplitudes is essentially the same, but an estimate of the phase change as a function of frequency is provided. For larger slopes, differences appear in the analytical form as well as in the numerical results. The Rayleigh expression has advantages above cutoff, while a new approach seems better before and just after cutoff.
An acoustic signal from a cw source towed near the sea surface produces a Lloyd’s mirror type of pattern. The signal received on a six-hydrophone moored array gives a record of this three-dimensional pattern. A comparison of the observed data and calculated pattern using the characteristics of the ocean provides some insight into transmission in a region where the velocity is depth dependent.
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