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This chapter will extend the results from Chapter 10 by using more advanced analytical methods for calculating acoustical quantities such as mutual radiation impedance. Before fast computers were available some of the results obtained by analytical methods had limited usefulness when they were expressed as slowly converging infinite series or integrals that required numerical evaluation. Now such series and integrals can be evaluated more easily. In some cases the analytical methods give more physical insight, or can be reduced to a simpler form, than the strictly numerical methods.

Electrical and acoustical measurements are made on transducers to determine performance characteristics and parameters for comparison with goals and theoretical models when the latter are available. In this chapter we discuss the procedures and means for making such measurements [1–]. Admittance or impedance measurements are normally made first under air loading (which simulates a vacuum) and then under water loading, often at various hydrostatic pressures, temperatures, and drive levels. Measurements of the transmitting response, source level, efficiency, receiving response, beam patterns, and harmonic distortion of transducers and transducer arrays are usually made in the far field, where spherical spreading holds. However, in some cases measurements can be made in the near field and projected to the far field through extrapolation formulas. Measurement is the important final step in evaluating the performance of all transducers.