The impulse response and time dependent force on a baffled circular piston and a sphere

Abstract

The time dependent force on the surface of an acoustic radiator which is vibrating with a uniform velocity is expressed as the convolution of the surface velocity with an appropriately defined impulse response. Since the impulse response is equivalent to the inverse Fourier transform of the acoustic radiation impedance, the impulse response for particular vibrators whose radiation impedance is known can be obtained directly from the impedance. To illustrate the approach the impulse response for a baffled circular piston and a pulsating sphere are obtained from their respective radiation impedances. Both impulse responses exhibit the same initial behavior, i.e., a Dirac delta function at time zero; however, their subsequent time histories are considerably different. The time dependent forces on both the piston and sphere are investigated for pulsed velocities and the results are compared to classical steady-state results.