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BELL SYSTEM TECHNICAL JOURNAL 



spherical wave, in place of the plane wave employed for a straight 

 tube. For this case we can write ^ for a simple harmonic wave 





df 



dr~ 



d(p , p 



-T— and — = (p, 



or po 



where (p is the velocity potential, r] the linear velocity for the spherical 

 wave, p the pressure, p the average density of the medium, and r the 



1.0 1.2 



VALUE OF ^ 



Fig. 6 — Attenuation~constants for a band pass type of filter 

 distance from the apex of the cone. The solution for this case is 



Tip = A sm-^r -\- B cos -^ r. 



Hence we can determine 77 and p as 



= A 



. CO CO OJ 



sm-^r -^cos-?;^ 



+ B 



CO CO . CO 



cos-^r ^sm ^r 



and 



p = icop 



^ sm -^ r + -D cos -^ r 



If now we set 77 = when r = X2 and determine the ratio of p/rj at 



* Lamb, "Dynamical Theory of Sound," p. 206. Rayleigh, "Theory of Sound," 

 Vol. II, p. 114. 



