REGULAR COMBINATION OF ACOUSTIC ELEMENTS 



in 



An example of the type of characteristic obtained, is given by the 

 special case where the lengths of both tubes are the same and equal to 



VALUE OF ^ 



Fig. 5 — Propagation constants for a high pass type of filter 



3L. If 6*2 is the area of the open tube and S-i that of the closed tube, 

 then neglecting dissipation, we find 



1. r 2coL 1 



cosh r = cos —^ — h :r-^ 



^2 



S, 



ScoL 3coL 



tan -yr- cot -yr- 



sm 



2coL 



A plot of A, the attenuation constant, for several values of S^/Si and 

 Ss/Si is given in Fig. 6. 



D. Other Types of Sidebranches 



We have so far considered only the characteristics obtained where we 

 employ straight tubes. A number of cases can be solved in which the 

 elements employed are not straight tubes although we cannot take 

 account of the viscosity dissipation in these cases. As an example, the 

 characteristics of a filter will be worked out, which employs a straight 

 tube for the conducting tube and conical tubes closed on the end 

 for the sidebranches. We can make use of equation (21) to determine 

 r and Zq, if we insert the proper value of Zs for the conical tube. 



It is evident that for a conical tube, the proper type of wave is a 



