A note on the frequency correlation of the fluctuations of acoustic waves in a random medium

An expression for the frequency-correlation coefficient for both the amplitude and the phase fluctuations of two plane waves propagating in an unbounded inhomogeneous medium is derived. The result obtained is valid for large-scale inhomogeneities and is thus applicable to ocean acoustics. The theoretical treatment in the derivation follows closely some theoretical work presented by Chernov on the longitudinal autocorrelation of the fluctuations in a single plane wave. For the results obtained, a simple physical picture of frequency correlation in relation to spatial correlation, in terms of average phase differences along propagation paths, is presented. It is established that within the "wave-theory" region the frequency-correlation coefficients for both the phase and the amplitude fluctuations are identical. The coherent bandwidth, which is obtained from the "width" of this correlation coefficient, is found to be inversely dependent upon range. In the "ray-theory" region there is complete frequency correlation. Applications of frequency correlation in nonlinear acoustics and underwater communications are briefly discussed.