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In the course of working with certain sonar transmitting array problems, we must determine the transfer matrix relating element heat velocities to amplifier input signals. We require this matrix to predict element head velocities as a function of a given distribution of amplifier input signals and vice-versa without resorting to scale-model or prototype array studies. The purpose of this memo is to present the development of this transfer matrix for several types of modularly-driven transducer arrays. The simplest type of modularly-driven array is that with only one element per module. The development of (K sub ij) for this type of array is presented first to prepare the way for more general developments for several types of modularly-driven arrays. We would like to emphasize at this point that the transfer matrix used in this memo may be computed utilizing data from available computer programs. No significant modification of existing programs is required; rather a new program must be written which would use several available programs in effecting final computation of the (K sub ij) transfer matrix.

It is well established that given the computations for predicting the performance of a transducer array at a frequency band centered at f sub o one can easily scale the entire problem to a new frequency band centered at f sub s. The purpose of this note is to document with simple examples a recipe for performing such a frequency scaling of the entire problem and thereby help avoid wasting time re-thinking this procedure whenever it is needed. No attempt will be made to treat the subject in general or in depth.