Optical and interferometric studies on oscillating quartz crystals

Abstract

The methods of investigation in the present work deal with: firstly the calculation of the frequencies of vibration of the different modes of extensional vibrations both radial and torsional of circular, solid and annular, plates as predicted by Love's theory. These are experimentally examined and empirical rules governing the frequencies are evolved. Secondly, the physical form of the vibration at the different calculated resonant frequencies is observed. This is carried out either by investigating the position of the nodal and antinodal regions on the vibrating surface or by investigating the distribution of stress inside the body of the vibrator. Three methods of observations have been used, namely, the interference method and this gives a measurement of displacements in the normal direction to the plate surface, together with an exact measurement of the surface amplitudes of the vibrating plate. Chapter IX is dealing with amplitude measurements. The powder method and it will be shown that it gives indication of both vertical and horizontal displacements. The third method used for the present investigation gives the stress distribution within the specimen provided the specimen is sufficiently thin. It is shown that it is generally unreasonable to expect any one method of observation to give a reliable solution to the type of motion and to the mode of vibrating body. The three methods together should be used in order to give a sound information about the vibrating motion; otherwise a misleading representation of the state of vibration is likely to arise.A practical agreement has been found between the theoretical and observed patterns for the second and third methods of investigation. The interference method did not offer a good correlation between theoretical and observed patterns; since it is always coupled to flexural modes of particular symmetry. However, the method gives an exact measurement of the surface amplitudes. The measurements require no calibration.