45 



BELJ. SYSTEM TECHNICAL JOURNAL 



These cases are sufficient to illustrate the method of calculation, but 

 there is one other important case for which I desire to give the results 

 as this is the case handled experimentally by Kennelly and Upson. 



Case III — Diaphragms Connected Acoustically by a Tube of 

 Air of Uniform Cross-Section with an 

 Air Chamber at Both Ends 



In this case the two diaphragms are connected acoustically by the 

 air, but since the tube has considerable length phase differences exist 



f 



y ////////////// ^ ^ .• f ^ '/.• ;;;/ / 



■*x 



I 



'/////// /yirr777-r7-z^//// ///// / 



O 



'Vt 



R - 



Fig. 9 



at different points along it. The connections are shown schematically 

 in Fig. 9. 



The equation of motion for the receiver diaphragm is 



Zi — QRdpR _ Zi 



y = 



(33) 



and for the transmitter diaphragm is 



QrdpT 



(34) 



where dpR and dpr are the pressure variations in the air chambers 

 at the receiver and transmitter ends of the tube respectively. 



The equations of motion for a gas in which the movements are 

 small and in only one direction and in which the fluid friction is 

 neglected are as follows : ^ 



dr- ^ dx^' 



dp 

 P 



dj) 

 It' 



(35) 

 (36) 



*See Rayleigh "Theory of Sound," Vol. II, pp. 14 and 15, 49 and 50. 



