U L T H \ S O X I C V T }i \< A T IONS 



319 



One of the best cuts for this purpose is the a;-cut crystal iUiistrated 

 in Figure 6. The faces normal to the x axis are those to which the 

 alternating electrical field is applied and the resultant motion of the 

 crystal is one of alternate expansion and contraction between the two 

 faces. This means that, if one face of the crystal were cemented to a 

 solid block, the other face will move up and down with a pistonlike 

 action. While the amplitudes of vibration are generally small for 



^ axis 



Fig. 6. Arrangement of crystal axes in an A'-cut quartz plate. An alternating 

 potential applied to the electrode surfaces will cause contraction and expansion in 

 thickness d. 



the reciprocal piezoelectric effect, the power delivered can be large 

 owing to the high frequencies involved. 



For an ar-cut crystal, the type of vibration set up by an alternating 

 electric field is similar to that produced in a magnetostrictive rod. 

 That is, the crystal has a natural period of vibration determined by 

 its elastic constants and its thickness (in the x direction). The fun- 

 damental frequency of vibration is: 



/ = (c/p)"/y2d 



(13) 



where, for x-cut quartz, c = 85.46 X 10'" dynes per square centimeter, 

 p = 2.65 g. per cubic centimeter, and d is the thickness in centimeters 



