A Theory of the Crystal Transducer for Plane Waves

Abstract

From the equation for propagation of acoustic plane waves through a solid medium, expressions are derived for the vibrational amplitude, radiated power, and electrical admittance of a plane-wave crystal transducer. The transducer consists of crystals, backing, and diaphragm, radiating into any medium. The crystals may be an assemblage of flat bars vibrating lengthwise, or there may be a single flat crystal plate, or mosaic of plates, in thickness vibration. The equations take account of attenuation in the diaphragm, but not of attenuation in crystals and backing, nor of the effects of cement layers and lateral stresses between crystals. The general equations, which are valid at all frequencies and for all thicknesses of backing, crystal assemblage, and diaphragm, are specialized to the case in which the backing is air. Special attention is given to those frequencies at which the crystals, or diaphragm, or both, are in resonance. Some typical theoretical curves are shown, and a graphical method is described for the rapid plotting of curves.