MODES OF MOTION IX QUARTZ CRYSTALS 



53 



the type which presents itself in the xylophone, the chime type door bell, 

 and various other vibrating reeds or bars. Fig. 6.1 shows the general type 

 of motion of a bar free to vibrate in flexure. The displacement takes place 

 in the direction of W and the wave is propagated along the length. A 

 flexure mode is one in which the center line does not change length. The 

 type of motion associated with the first order, or fundamental, of a bar free 

 to vibrate on both ends is shown in Fig. 6.1 with a dotted figure superim- 



1 ST 



2 NO 



3 RD 



Fig. 6.1 — Motion of a bar in free-free flexure. 



posed to show the motion in the opposite phase. The straight bar then 

 w^ould be distorted first in one direction and then in the direction of the 

 dotted figure. In the case of the second mode of vibration, it will be noticed 

 that it consists essentially of two of the fundamental mode types joined end 

 to end. This is not strictly the case, but serves to illustrate the motion. 

 The dots shown at various points on the bar show positions of zero motion 

 or nodes. In the case of the fundamental mode, there are two nodes and in 

 the second and third there are three and four respectively. One point of 



