Modes of Vibration in Piezo-Electric Crystals

The presence of nodes and antinodes on the surface of oscillating quartz crystals have been discovered. The symmetrical arrangement of these nodal points permits a study of the modes of vibration in the crystal plate and the use of the following formulas for determination of the velocity of sound waves through quartz and Young's modulus. V = F2T e= V
²
D. where V is the velocity, F the frequency, T the thickness of the plate, e Young's modulus and D the density. The value obtained for V was 5733 meters per second while 8.785X10
¹¹
C. G. S. units represents Young's modulus for plane parallel to X-axis dimension.