R. L. Pritchard's classic mutual impedance contribution.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Dipole transducer enhancement from a passive resonator.

A passive resonator model for enhancing the low frequency performance of dipole transducers is presented using a spherical wave function model. It is shown that because the near field response of a dipole has the same on-axis low frequency dependence as an equivalent monopole, it can effectively excite a nearby monopole passive resonator and do this with enough strength to significantly modify the response of the system. Sample results are presented to demonstrate the performance enhancement and to illustrate the conversion of the dipole beam pattern to a nearly omni-directional beam pattern.

Thermal model for piezoelectric transducers (L).

A lumped parameter equivalent circuit basis for calculating and allocating heat power sources in a transducer is presented along with experimental results. The simple model allows heat power calculations at resonance based on readily attainable parameters for transducers with uniform fields. Measured and finite element analysis of steady state thermal results are compared for the monopole mode of the single crystal driven modal transducer projector. The model serves as a physical and computational aid in the evaluation of piezoelectric transducer heating and may be used for evaluating highly coupled single crystal as well as ceramic piezoelectric transducers.

Transducer figure of merit (L).

An alternative formula for determining the volume-referenced, projector-transducer figure of merit, FOM(v), is developed allowing an evaluation based on well known parameters that may be readily calculated or measured. This formula is also reduced to the special case of piezoelectric or magnetostrictive materials, allowing a FOM(v) comparison of transducer materials in addition to an evaluation of specific transducer designs. Sample results are given for transducer materials alone and a PZT-8 driven modal projector transducer operated in the monopole mode.

The modal projector.

The superposition of acoustical modes radiated from a transducer can provide directionality from a compact projector. This paper presents the foundation, as well as examples, of piezoelectric ceramic, piezoelectric single crystal, and magnetostrictive versions of this "modal projector." Measured and analytical, as well as finite element analysis modeled, results show good agreement and establish this transducer as a viable source of intensity with the advantages of an improved directivity index, reducing the power needed from a compact source.

A tri-modal directional transducer.

Acoustic transducers made from piezoelectric ceramic cylinders usually exploit the breathing or omnidirectional (omni) mode of vibration. However, with suitable voltage distribution, higher order extensional modes of the cylinder can be excited which produce directional radiation patterns. These modal radiation patterns can then be combined to synthesize desired beam patterns which may be steered by incrementing the excitation. This paper describes a model for the combined acoustic response of the extensional modes of vibration of a piezoelectric ceramic cylinder, a method of synthesizing a desired radiation pattern, and an experimental implementation of a directional transducer that uses these techniques. This tri-modal transducer is broadband and directional with a frequency independent beam pattern yet simple, small, and lightweight.