Ultrasonic waves have become an important research technique in many fields, including chemistry, mechanics, and others. Piezoelectric crystals excited by a source of alternating voltage are commonly used as a method of producing ultrasonic mechanical vibrations for such purposes. Hence it is often necessary that crystal transducers be designed, and to those unfamiliar with the theory of piezoelectricity, such a design problem may entail time-consuming research. The present paper is intended to co-ordinate the several approaches to the design problem and to present a practical method for designing quartz-crystal transducers for ultrasonic frequencies.

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