The reception of amplitude-modulated narrow-band signals of a noisy carrier is considered for propagation in a medium with absorption which depends on the frequency of a background of noisy interference. The purpose of the work is to optimize analytically the frequency for receiving the amplitude-modulated stochastic acoustic process. The efficiency of reception depends very much on this frequency. An optimization problem was formulated and solved. The power criterion, namely, the overall signal-to-interference ratio at the detector output, was used as a criterion of optimality. Two important practical cases were considered: (1) The carrier is narrow-band; and (2) the carrier is broadband. New expressions have been obtained for optimum frequencies.