The output spectrum of a controllable swept-frequency acoustic source at a given frequency can be controlled by making the rate of change of frequency equal to the desired output power spectrum divided by the squared envelope amplitude of the source output signal, both measured at the time after the start of its frequency sweep at which the sweep frequency passes through the given frequency. The system and method can also be used to correct for propagation effects outside the source by dividing the desired spectrum by the propagation effect. The method can further be used either to obtain an output spectrum of a desired shape from a source operating at maximum output or to design a sweep of a minimum feasible duration that will result in an output spectrum of a specified shape and with a specified amplitude.