PRINCIPLES OF MOUNTING QUARTZ PLATES 189 



cause very little. The wave-length of a sound wave in air may be readily 

 computed, and since we arc interested in multiples of one-quarter wave- 

 length, it is desirable to determine these for a given frequency. This can 

 be computed readily from equation S.3, 



4 4/ 



where v is the velocity of sound in air at room temperature and pressure and 

 equals 33,000 centimeters per second. For example, a quarter of a wave- 

 length at 5 miCgacycles is given by 



X 33,000 ._.,. 



7 = A ., - -.y .f^r = .0016:) cm 

 4 4 X :) X 10^ 



which indicates that if / of Fig. 8.10 were made equal to this or odd multi- 

 ples, there would be very little efifect of the electrode on the crystal and if / 

 corresponded to even multiples of a quarter wave-length, we would expect 

 considerable damping. Some measurements of this effect have been made 

 with a low frequency A T-cut quartz crystal and are shown in Fig. 8.12. The 

 sound wave generated by an /IT-cut probably results from flexure waves 

 generated by the high-frequency shear wave. It will be noted that when the 

 airgap is equal to even multiples of a quarter wave-length, the activity is 

 considerably reduced. Further, it will be noticed that airgaps in the order 

 of 1/8 of the wave-length may be used and produce very little effect. Since 

 a large airgap reduces the piezoelectric coupling it is desirable to keep this 

 about 1/8 of a wave-length as a maximum unless, in special cases, a reduction 

 in piezoelectric coupling may be tolerated. 



