Evaluation of mutual radiation impedances between circular pistons by impulse response and asymptotic methods

A general approach is presented to evaluate the mutual radiation impedance between circular pistons of arbitrary size and spacing in an infinite rigid planar baffle. The impedance is expressed as a Fourier transform of a generalized impulse response which is defined by an integral relationship. Although the integral must, in general, be numerically evaluated, several special cases of interest can readily be evaluated by using asymptotic techniques. Several asymptotic expressions for the mutual radiation impedance are developed and their limitations are noted. Numerical results are then presented for the generalized impulse response and mutual radiation impedance corresponding to pistons of equal size and arbitrary spacing. The time domain characteristics of the generalized impulse responses as a function of spacing are noted and related to the frequency characteristics of the mutual radiation impedances as a function of spacing. In addition, the accuracy of a simple closed form expression for the mutual radiation impedance is presented as a function of normalized frequency and spacing.