A HIGH EFFICIENCY RECEIVER . 151 



of the tube from a' to and from a to had a radial velocity equal to 



2irro 



I. [i-^. ].'"'. 



The velocity potential at a point, P, at a distance y from a, if /-o is 

 small compared with the wave-length of sound, is then 



I 



R 



a 



fP 



■r-^ 



— r 



-y- 



^y 



/ ro'^^ 



Fig. 10. 



Qik{ct—y—r)fJ^y 



+ 



'-W 



To'k 



oil<{ct—y—2R+r) fly 



lo, 



where c is the velocity of sound and 



c 



or 



<Py = A 



2tne' 



'k(ct-y-R) 



where 



— irtfk^ 



A^[X+^VoskR+{2-^, 



If we take the real part of 



d^y 



dt ' 



we get the instantaneous pressure at the point, P, where p is the density 

 of the air. This gives 



Py ^ T^ ■ -4 COS k{ct — y — R). 



