Resonance in crystal beams of sodium-ammonium seignette salt

Abstract

It has been noticed by several observers that, with longitudinal oscillations in certain crystal beams, on keeping the length constant and gradually decreasing either the breadth or thickness, a sudden change of considerable magnitude may occur in the wave-length. This has been attributed to some resonance effect. Lack (1929) describes interesting results obtained with rectangular quartz beams of 30° cut. The X axis, as with Voigt, coincided with an electric axis and constituted the length direction of the beam. The breadth was parallel to the optic axis. With such a beam there is a low vibration frequency depending upon the length, and a high vibration frequency varying inversely as the thickness, the field being applied in the direction of the thickness. A square plate was used, and on gradually reducing the thickness, several discontinuities occurred on plotting the wave-length against the thickness. According to Lack these discontinuities occurred at frequencies that could be identified with har­monics of the frequency which the crystal would have if it were vibrating in the direction of the length. That is, the longitudinal oscillation along the length could affect the frequency which was supposed to depend only on the thickness, so that the system acted as two coupled electrical circuits, although the two sets of oscillations were in planes at right angles. Somewhat similar results have been obtained for quartz beams by Hitchcock (1930). He used the Curie (or perpendicular) cut, where the length is perpendicular to an electric axis and the thickness parallel to it, whilst the breadth is parallel to the optic axis. Hitchcock showed that the frequency of oscillations along the length suddenly changed in value on decreasing the breadth.