PRINCIPLES OF MOUNTING QUARTZ PLATES 181 



where v = velocity in cm. /sec. 

 d = diameter in cm. 

 I = length in cm. 

 m = 1.875 for first mode 



= (n-l/2)Tr for 2nd, 3rd, etc. 

 From this we can compute the length necessary for a given rod at a given 

 frequency and use this for the design of the clamping rods. This length is 

 given in equation (8.2) for the case of a 100-kc crystal using phosphor bronze 

 rods 1 millimeter in diameter 



/^ 



c = 1.8/:) 



87r X 10^ (8.2) 



= ,225 cm 



This corresponds to the case of Fig. 8.3A. For the case of Fig. 8.3B, the 

 length is given by 



I = .567 cm 



Using this same diameter rod, if we should go to a considerably higher fre- 

 quency, for example 5 megacycles, the value of / would be extremely small 

 even for the case of Fig. 8.3A and would be somewhat sm.aller than the 

 diameter of the rod. As mentioned before in Chapter VI, the simple for- 

 mulae that apply in the case of fiexure are only for the case of a long thin rod. 

 When the length becomes equal to or less than this diameter, it is very prob- 

 able that the support member should be designed as though it were vibrating 

 in shear. These follow well-known rules and are only mentioned here in 

 case designs for high-frequency crystals are contemplated using this method. 

 The design of rod-supported crystals following this procedure has not been 

 carried on to a large extent in these laboratories because, at present, the 

 wire-supported crystal appears to have many advantages. A great deal 

 more of the work in regard to resonating supports has been done for the 

 case of the soldered lead type^ 



8.2 Wire Type Supports 



The theory of resonating supports involving soldered leads on crystals is 

 very similar to that just discussed for the case of rods. There are two 

 additional elements that we have here that are not present in the case of the 

 rod, these elements being the actual solder connections that fasten the wire 



' The presence of standing waves on the lead wires of CT crystals was found experi- 

 mentally by Mr. I. E. Fair. 



