An acoustic pulse propagating the ocean encounters weak thermal patches that scatter energy. If these patches are moving with a mean current perpendicular to the direction of propagation, a temporal fluctuation in the pulse-averaged amplitude occurs. This study calculates the temporal frequency spectrum of the pulse-to-pulse amplitude fluctuations and finds the result in terms of a frequency convolution of Tatarski's CW spectrum found for the electromagnetic case, and the spectral distribution of the initial pulse. The result easily generalizes to amplitude, phase, and phase-difference spectra, for plane, spherical, and beam-wave pulses.