468 Propagation of Disturbances in Elastic Media. 



at any instance in the disturbance. Let V be the velocity of 

 propagation of the disturbance. 



Take two planes A and B drawn across the bar. 

 Consider the momentum generated inside the space A B by 

 the passage of the disturbance into A B. 



In the passage of the disturbance across A the mean force 



acting on AB is SM— , and is upwards. And the time for 



x x 



which it acts is ^. Thus the momentum generated is 



Also, since a portion of length V is displaced upwards by 

 a distance I in one second, the momentum is 



SVZd. 

 Thus we get V2 __ M 



T 



That the disturbance travels unchanged in form may be 

 proved as in the case of a longitudinal disturbance, by show- 



/M 



ing that when the velocity of each part is a / -7, then the 



forces called into play at each point are just the necessary 

 forces to maintain the disturbance unchanged. 



The case of two media may be investigated as before. 



Transverse Disturbance in Stretched String. 



Suppose we have a string of which m is the mass per unit 

 length, stretched with a tension T. Let a transverse disturb- 

 ance be sent along it from left to right. Let the disturbance 

 be such that each point of the string is displaced upwards by 

 a distance I. Let x be the length of the string involved at 

 any instant in the disturbance. Let V be the velocity of 

 propagation of the disturbance. 



A B 



Take two points A and B on the string. 



Consider the momentum generated between A and B by 



