The Duguay, Hargrove, Jefferts frequency translation experiment is analyzed in terms of superposition of side bands. It is shown that a Gaussian input pulse leads, in a good approximation, to a Gaussian output pulse translated in frequency, so long as the modulation index is not so large as to lead to a translation, in units of the inter‐mode spacing, of the order of the cube of the number of modes of appreciable amplitude in the input pulse.