76 



BELL SYSTEM TECHNICAL JOURNAL 



In evaluating 7n, account was taken only of the rotary and lateral inertia so 

 that some error is expected at the larger ratio of axes. The curve of flexure 



crosses the shear curve at - = .76, a condition which we know to be non- 



l 

 compatible since these two motions are coupled. From the theory of coupled 

 circuits we can determine the displacement of two uncoupled frequencies as a 

 result of the coupling, through the relation 



fU = Wl +/; ± V(/i - fff + ^kYj}] 



6.17 



300 



280 



260 



240 



220 



200 



180 



160 



140 



120 



100 



80 



60 



40 



20 



01 02 3 04 05 06 7 08 09 10 



Fig. 6.13 — Effect of coupling on the plate shear and the second flexure mode in an 

 ylC-cut quartz plate. 



where f, = uncoupled shear frequency, 

 // = " flexure " 

 k = coefficient of coupling. 



The coefi&cient of coupling in this case may be defined as the ratio of the 

 mutual to the square root of the self compliances of the two vibrating sys- 

 tems. As mentioned before no derivation has yet been made to indicate the 

 relation between the coupling between these two forms of motion and the 

 physical constants of the medium in which the vibration occurs. It is 

 necessary to assume some coupling factor which will produce that observed 



