Approximate Scaling Laws of Acoustic Array Interaction

For a fixed set of parameters, computing the performance of an array of H transducers when taking acoustic coupling into account usually involves the solution_of a real matrix equation of order 2N.If N is large, the computation for just one set of parameters can be a considerable task.In array interaction studies many parameters are variable, and the computational effort to cover even a limited range of variables can be formidable indeed..One approach to reducing the magnitude of effort required is to search for scaling laws, even of an approximate nature, which will enable conlusions drawn from a study of one array to be applied to a family of arrays.r THE SCALING LAWS _This paper, which is based on Ref 1, describes the derivation of approximate scaling laws for planar arrays of piezo electric elements vibrating either within an infinite, plane, rigid baffle or'with no baffle present; the transducer faces are deemed to be rigid and circular, with diameter less uuxk/Q and, for convenience, the medium is assumed to be water.All transducers of an array are presumed identical.The several scaling laws which are deduced can be applied in combination, providing the restrictions applicable to each individual law are complied with.'