The method of determination of the optimum frequencies for active sonar without knowledge of the absolute values of the sonar set parameters, but only of their frequency dependence, appears to have been originated by J. W. Horton in about 1945 and is to be found in his recent text [J. W. Horton, Fundamentals of Sonar (United States Naval Institute, 1957), pp. 317–324, 344–352]. This theory has been simplified and extended to include search rate and the ratio of echo to noise plus reverberation. The inclusion of search and reverberation only slightly modifies the results obtained by maximizing echo-to-noise ratio alone because of the dominating effect of the frequency dependence of the exponential attenuation term in the transmission loss. The exact frequency dependence of the attenuation is critical as a result of this dominance. The slope of the optimum frequency vs range curve on a log-log plot is the negative of the reciprocal of the frequency exponent of the attenuation.