APPROXIMATE NETWORKS OF ACOUSTIC FILTERS 



?,?>?> 



what type of side branch is used, the resonances of the latter deter- 

 mining the frequencies of maximum suppression. 



The equivalent electrical circuit for an acoustic filter, was shown in 

 a previous paper ^ to be two lines shunted by the impedance of the side 

 branch. This representation is shown on Fig. 2. To obtain a lumped- 



Fig. 2 



constant representation for this network, it is necessary first to con- 

 sider the lumped-constant representation of a line, which is discussed 

 below. 



A. Lumped- Constant Representation of a Line 



In a previous paper - it was shown that the propagation constant of 

 a tube is given by the equation 



p-. _ 



-^[(•-tVS)-^V£^]. ^'^ 



while the characteristic impedance is given by the expression 



Z = 



pc'P 



(2) 



In these equations co is 27r times the frequency, c the velocity of sound, 

 Po the perimeter of the tube, 5 its area, p the density of the medium 

 and 7'-, a constant 1 elated to the viscosity, which for air has the value 

 4.25 X 10-* in c.g.s. units. 



A tube is the analogue of an electric line with distributed resistance, 

 inductance, and capacity. No quantity corresponding to leakance is 

 present. To determine the values of these quantities, use is made of 

 the well known equations for a line 



Z = 



R -f jcoL 

 G + jcoC ' 



P = V(i^-f jcoL)(G-f jcQ, 



(3) 



where R, L, G and C are respectively the distributed resistance, induc- 

 tance, leakance, and capacity of the line per unit length. Comparing 

 - Loc. cit. 

 22 



