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BELL SYSTEM TECHNICAL JOURNAL 



If we assume no dissipation, and substitute the values of ai and Zi 

 given in section (I), we have 



cosh r = 



cos 



26'i cot ( ^l 



(26) 



^Poyp 



tan -^ L 



CO , 



cot-^/ 



(27) 



An example of the type of filter obtained by acoustic means, is given 

 when we let / = 2>L. Fig. 3 gives a plot of the value of V for several 

 ratios of S2/S1. Fig. 4 shows the corresponding values of the specific 

 characteristic impedance Zq. 



PLOT OF EQUATION- 



5? SInUuA/cn 



FULL LINES GIVE VALUES OF A 

 OOTTEO " 



Cosh r'CoshfA*lB)- [cos ^^ 



Fig. 3 — Propagation constants for a low pass type of filter 



A knowledge of F will determine the ratio of pressures or volume 

 velocities, if we have an infinite sequence of sections, or if we terminate 

 a finite sequence in the impedance Zq. If however the terminating 

 impedance is not the characteristic impedance, e~^ no longer represents 

 the ratios of pressures between adjacent sections. 



i 



