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.