A theoretical model is presented for evaluating the transient velocity potential and pressure fields radiated by a pulsed planar piston set in an infinite rigid baffle and having an arbitrary spatial velocity distribution. The method is based on the development of a generalized spatial impulse response function which describes the velocity potential, either at a point or averaged over a finite receiving surface, resulting from the velocity impulse excitation of a uniformly or nonuniformly vibrating piston source. For the specific case of a circular source and receiver this function is plotted using several source distributions and receiver sizes. Then corresponding plots are presented for two piston velocity waveforms: a Gaussian pulse and a Gaussian-modulated sinusoidal burst. These plots are compared and the effects of a nonuniformly vibrating source and finite receiver are discussed. Lastly, a previous solution by Schoch, in which the field of a rigid piston is separated into geometrical and boundary diffraction waves, is extended to account for a nonuniform source, and the relationship of this more general result to the present approach is illustrated.
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Gerald R. Harris (1981) studied this question.