ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 2OI 



beginning. With this end in view let us consider a bend of any 

 shape, and let us imagine that this bend is traveling along the 

 string to the right (or left) at any velocity v. For example, one 

 can make a bend of definite shape travel along a stretched string 

 by threading the string through a bent tube and moving the bent 

 tube along; but the state of affairs would be entirely unchanged 

 if we imagine the bent tube to be stationary and the stretched string 

 to be drawn through it, as indicated in Fig. 138. It is assumed 



Fig. 138. 



that the string slides through the tube without friction. The 

 tension of the string alone would push the string against side d 

 of the tube at any point p, and the motion of the string (in the 

 absence of tension) would throw the string against side c of the 

 tube because of centrifugal action. Let r be the radius of 

 curvature of the bent tube at p. Then the particles of the 

 moving string may be thought of as traveling along a circular 

 path of radius r as they pass the point p. Therefore* the side- 

 wise acceleration (in the direction of the radius r) of the string 



v 2 

 at p is . Consider a, very short piece of the string of length 



v 2 



ds and whose mass is m-ds. Then m-ds X is the side 



r 



force (towards the center of curvature of the bent tube at p) 

 which must act on the short piece of string to produce the specified 



v 2 

 acceleration . If the string has no tension, then all of this side 



force is exerted by the side c of the tube. 



The stretched string near p is like a barrel hoop under tension, 

 and its tension T produces on the element ds a side force (draw- 



* See Franklin, MacNutt and Charles's Calculus, Art. 50, page 70. 



