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BELL SYSTEM TECHNICAL JOURNAL 



the forces exerted on the upper and lower surfaces are equal and opposite. 

 That downward on the right face exceeds that upward on the left by 



— ( — I A.T^. By ex- 

 dy\2) ^ 



tending the argument to three dimensions it is easily shown that the total 



Ty (I ^^) ^^' 



SO the force in the z direction is 



Fig. 2 — Diagram showing the forces exerted by an element of the medium through 

 its surfaces. 



force isV X 



PoAr* — , so 

 at 



i-j ^o<?. If po is 



the density of the medium this force must equal 



V X 



T 



dq 



which, since q is small, reduces to 



Po 



dq 



dl 



(8a) 



From this and (6a) the velocity of propagation is {vq/poY and the char- 

 acteristic resistance is {poVoY • In a plane wave the displacement is normal 

 to the direction of propagation. The stress is a tractive force per unit area 



— acting in a surface normal to the direction of propagation. It is in the 



direction of the velocity and in phase with it. 



