A new approach to the derivation of the impulse response of a rectangular piston

In this work, a ‘‘spatial convolution’’ approach is employed to derive an exact solution for the impulse response of the uniformly vibrating rectangular piston. While in the classical approach, proposed by Stepanishen [J. Acoust. Soc. Am. 49, 1629–1638 (1971)], the impulse response is regarded as a function of time for a fixed field point location, here the impulse response is regarded as a function of the spatial coordinates, for a fixed time instant. The introduction of ‘‘line masses,’’ and the use of their integral properties, allow a simple derivation of the analytical expression of the impulse response. Computational results show a complete agreement with previously reported data for the same source geometry and field point locations. The diffraction analysis is also extended to the nonuniformly vibrating rectangular piston.