344 Mr. R. H. M. Bosanquet on the Theory of Sound. 



two streams of sound which are propagated from it in both 

 directions. 



Let the axis of the cylinder be the axis of x, the origin the 

 position of rest of the disk, and y the displacement at any 

 point. 



Then, on the right, where the transmission is forward, 



y^-Asin— (vt— as) } 



dy 1 27rA 2-7T , N 



-~— — — cos—- (vt — x). 



dx \ X v / 



And on the left, where the transmission is backward 



A • 2tT / . 



y 2 = A sin — (vt + x), 



dy 2 2ttA 2-7T , x 



-p - -xr- cos -— (vt + x). 

 ax X X v y 



And the difference of pressures on the two sides of the disk, 

 where x=-0, is 



\ax ax / x=o 



or, since - = -> 



X T 



2x1-411x2^ cos 2tt- 



X T 



The work done by the disk in passing through the space dy 

 against this difference of pressures is this difference x dy, and 



(dy\ 2ttA t 

 (-£) = cos 2tt- ; 



\at / z=0 T T 



.*. work done in a quarter vibration is 



87r 2 A 2 r 4 „~7rt ", « ,„ 7T 2 A 2 



-Tcos 2 2^ = 

 Jo 



i-4n^-^ 



.*. work in a whole vibration 



2 A 2 



=4xl-4n^A; 



A. 



V 



and in a second, since vibration-number = - 



A, 



^xwn.(£). 



And this work produces two streams of pendulum-waves in 



