180 



BELL SYSTEM TECHNICAL JOURNAL 



be free to vibrate. This free end would then be in contact with the surface 

 of the crystal. If the bar were clamped and were of a length such that its 

 frequency of resonance equalled that of the crystal or approximately so, it 

 would require very little energy from the crystal to drive it, and any energy 

 received from the crystal would be rejected from the clamped end of the bar 

 and thereby kept within the vibrating system. This type of support is 

 shown in Fig. 8.2, where / = length of the rod and d its diameter. The 

 slightly rounded end is to allow the rod to seat firmly on the cr>-stal surface. 

 An enlarged view of Fig. 8.2 is shown in Fig. 8.3 and shows how the rod would 

 vibrate. Figure 8.3A shows the type of motion for the first mode of a clamp- 



Fig. 8.2 — Cantilever type mounting. 



I 



D 



N^' 



A B 



Fig. 8.3 — Type of motion in cantilever support mountings. 



free bar. Figure 8.3B shows the type of motion of the sam.e bar vibrating 

 in its second mode. This would indicate that for a given length of bar we 

 could use it at several difi"erent frequencies by simply using higher orders of 

 vibration. By using a clamp type mounting where the clamping rods are 

 designed as shown in Fig. 8.2, we may now have a mounting which at the 

 crystal frequency will allow the crystal to vibrate unrestricted but at the 

 same time provide a very secure clamp thus preventing the crystal from 

 moving about in its holder. To prevent rotation of the crystal about the 

 axis of the clamped points, more than two can be used provided they are of 

 the proper design. The frequency of a clamp-free rod in flexure is given 

 by equation (8.1) where m now has values different than in the case of free 

 free flexure. 



