REGULAR COMBINATION OF ACOUSTIC ELEMENTS 



265 



Combining with (15), we have 



Fs = Vi ( cosh aiL + ^^V^sinh aiL 



ZsSi 



- pxS, 



p3 = pi cosh aiL 



sinh aiL S^ cosh aiL 



'Li 



ZgSi 



— ^; — ^sinh a\L. 



(17) 



The pressures and volume velocities pi and Vi at one half the distance 

 between the first and second sidebranches are again 



(18) 



Vi = Vz cosh aiL — ^^-^sinh a^L, 



z . ^ 



pi = p3 cosh aiL — Fs-^sinh ajL. 



Combining with (17), we obtain 



/ Z S 



Vi— Vi[ cosh 2«iL + y^ „ sinh 2aiL 



pi= p].[ cosh 2aiL + ^y t! sinh 2a\L 



— ^tI— ^ I sinh 2aiL -\- „^' " cosh^ aiL 



Zo^l 



smh 2aiL + „ V smh^ aiL 



S, 



ZgSi 



(19) 



These equations apply to the first section of the filter. By comparison 

 with equation (10) we see that we can write equation (19) as 



Vi= Ficosh r -^sinh r, 

 Zo 



pi = pi cosh r — Fi-^sinh Y, 



(20) 



where 



cosh r = ( cosh 2aiL + r.y^ sinh 2aiL \, 



'1 + rf^ ^ tanh aiL 

 /Z5O1 



1 + 



ryt' I coth aiL 

 ZZ501 



(21) 



