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BELL SYSTEM TECHNICAL JOURNAL 



where X is given in millimeters. In this case it will be noticed also that 

 only even order flexures are strongly coupled to the fundamental Xy' shear. 

 The dependence of the flexure frequency on the shear coefficient can be 

 seen from these two cases. The direction of propagation is the same in both 

 cases (along the X axis) but the direction of particle motion is nearly at right 

 angles. It would be expected then that the frequency constant would be 

 highest for the case of the highest shear coefficient. Examination of equa- 



Fig. 6.17 — High frequenc\' flexure and shear resonances in a BT -c\xt quartz plate. 



tions 6.19 and 6.20 shows this to be true. In addition, the change in the 

 frequency constant is about the order of magnitude of the change in the 

 shear modulus in the respective planes of motion. 



6.43 Coupling between Low Frequency Shear and High Frequency Shear 



From an examination of Fig. 6.7 it can be seen that the coupling between 

 the low frequency shear (Zi) and the high frequency shear Xy' is related 

 by the s^f, constant. In the AC and BC-c\xts this reduces to zero but for the 

 AT and ^T-cuts it has a finite small value. According to section 6.3 the 

 frequencies of the plate shear modes are given by equation 6.8 but this 

 holds only for the case where ;;/ and n are small. When the third dimension 



