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BELL SYSTEM TECHNICAL JOURNAL 



the impedance Zs looking into the sidebranch. Another approxima- 

 tion used with organ pipes is to consider the tube extended by a length 

 .57 times the radius of the tube, and to consider this extended tube 

 terminated in a zero impedance. 



The impedance Zs for this case is from (10) 



-T7^ = Zs— Zl„ tanh aiV , 



V \ 



where /' is the corrected length of the pipe. Substituting this value 

 in equation (21), we have 



cosh r 



cosh laiL + 



Zi^^Si sinh 2 

 IZl^Sy tanh 



«2/' J ' 



Zl^S2 tanh a\L 



Zq — Zj 



1 + 



1 + 



lZi^,S\ tanh a4' 

 Zl.S^ coth aiL 

 2Zl,Si tanh aJt' 



For no dissipation these equations become 



2oiL 



(31) 



cosh r = 



COS 



2coL 

 ~C~ 



^ 2Si 



sm 



C 



tan 



VAtp 



1 + 



S2 tan ( -^ 

 25] tan ( -^ 



Si cot 



1 - 





25i tan f yr j 

 Fig, 5 shows a plot of T for several ratios of S^ISi, when V = 3L. 



C. 5awf/ Pass Type of Filter 

 The high pass type of filter discussed above can also be considered 

 as a band pass type of filter, in that an attenuation occurs at zero 

 frequency, then a pass band, and a second attenuation band. A 

 different arrangement of the pass bands can be obtained from the 

 structure shown in Fig. 2, by inserting two sidebranches at one junction 

 point, one of which is open at the outside end and the other closed. 



