A modal Pritchard approximation for computing array element mutual impedance

An investigation into the applicability and accuracy of Pritchard's approximation for closely packed transducer arrays is undertaken. A new, "modal" Pritchard approximation is developed, based upon normal modes of the acoustic medium, and is tested for arrays of acoustically hard spheres to ascertain its accuracy in determining the mutual acoustic radiation impedance between array elements. For ka approximately 1, it is found that the modal Pritchard approximation works quite well in approximating the mutual radiation impedance of a two-element array, even for relatively close spacing; but for arrays of three or more scatterers in close proximity the approximation may have relatively large errors. The effect of neglecting inter-element scattering is analyzed for the monopole-to-monopole scattering of various configurations of a three-element array and a sixteen-element double line array.