A probabilistic interpretation of the acoustic impulse response and applications to numerical calculations

Abstract

One approach used to estimate the radiation fields of acoustic radiators is the convolution method. This procedure evaluates the velocity potential by transforming the Rayleigh integral into the convolution of the radiator velocity profile with the so-called spatial impulse response of the radiator. It is shown that the impulse response is related to the probability density function of the acoustic path lengths and that calculations of the impulse response can proceed either from knowledge of the density or distribution functions of the radiator’s acoustic path lengths. Examples of the use of the method are shown to demonstrate that the approach leads to the same analytical expressions for the impulse response as obtained by traditional methods. It is shown that this probabilistic interpretation of the impulse response leads to readily evaluated numerical methods in the cases of radiator shapes which cannot be evaluated in closed form.