Ripple Formation in Kundt's Tube. 479 



considering as before between two spheres, 



T = K.E. of the spheres + £ R x V + Z R 2 3 w> 2 - wRsTW -=-£ 

 or putting R, = R 2 = R? 



V 



T = K.E. of the spheres + ^RV-ttRV -^— °- 



Now if we suppose the period of the sound-wave to be t, 

 then the velocity of the air at any point of the tube, at any 

 instant t, is 



t 



"J 



W = lV n COS 2lT 



T 



where w? -=the velocity at that point at the times £=0, r, 2t,... 

 Now to find the force between the two small spheres we 

 have 



at ow "ftc 



for the Z component of the force on one of the spheres. 

 Now T is expressed explicitly in terms of «7 ls w 2 , e u c 2 , and 

 so by using the equation for T, the equation of motion, and 

 the equation 



w — ir cos lir , 



T 



we can find Z. 



Thus z= d T _ BT 



dt ~dio o r ' 



a 2 - 



T=WM; 2 +^ : R 3 «o 2 -7rR 6 W 2 — ?, 

 where m is the mass of each sphere. 



V 1 



dT / 2-7T „ t;>6 ■/• A 



