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Equation 14 has been found to hold well as long as the change in 

 area is small while equation 12 holds well as long as the length of a 

 junction is less than half of a wave-length. 



III. Recurrent Filters 



With the aid of equations (10), (12), and (14), we can obtain the 

 propagation characteristics of any structure employing straight tubes, 

 sidebranches, and changes in area of conducting tubes. 



Among the simplest of these are recurrent filters. Fig. 2 shows an 



Fig. 2 — A typical acoustic filter 



example of this type of structure, a main conducting tube, with equally 

 spaced sidebranches. In order to make the structure symmetrical, 

 we let the distance L between one end and the first sidebranch equal 

 one half the distance between two sidebranches. We can then write 

 with regard to the first tube 



Vi — V\ cosh aiL — i^Si sinh axL, 

 p2 = pi cosh a\L — Vi -^sinh aiL, 



(15) 



where ai and Z^j refer to the conducting tube. For the junction, we 

 have by (12) 



Pz — p2- 



(16) 



