The lossy farfield pressure impulse response for a rectangular piston

Abstract

The impulse response of the velocity potential is useful for computing transient pressures in lossless media, especially for calculations in the nearfield region. Closed form expressions for the lossless impulse response of the velocity potential in the nearfield are available for circular and rectangular transducers and for several other geometries. A closed form lossless farfield expression is also available for rectangular transducers. Typically, when the effects of attenuation are introduced, the numerical calculation is performed in the frequency domain, and the time response is obtained with an inverse fast Fourier transform. To derive an equivalent analytical result directly in the time domain, all path lengths that appear in the denominator scaling term of the lossy diffraction integral are treated as constants, and a binomial expansion is applied to the path length that appears in the time delay term. The resulting analytical expression, which describes the lossy farfield pressure impulse response, is directly expressed in terms of maximally skewed stable probability density functions and cumulative distribution functions. Results are compared with the Rayleigh Sommerfeld integral, and excellent agreement is achieved in the farfield region. [supported in part by NIH Grant R01 EB012079.]