334 



BELL SYSTEM TECHNICAL JOURNAL 



(3) with (1) and (2), it is found that 



R 



L 



C 

 G 



P 



(4) 



pc 

 0, 



2 » 



neglecting small correction terms. These are the equivalent distrib- 

 uted constants per unit length of the pipe expressed in acoustic 

 impedance units. 



The representation of lines with distributed constants by means of 

 networks containing lumped constants has received considerable atten- 

 tion.^ With three impedances, either the T or it network representa- 

 tion shown on Fig. 3, can be used. 



/OL 



2S 



Ppi-Ml'^P^ 



X 



SL 

 PC' 



2 S 



X 



X 



PoL\/r^fpuj _ 



25^ V 2 



Fig. 3 



The impedances of short or open circuited lines can be represented 

 approximately by fewer elements than three. The first approximation 

 for a short circuited line is an inductance and resistance equal to the 

 sum of the distributed inductances and resistances of a line, while the 

 first approximation for an open circuited line will be a capacity equal 

 to the distributed capacities of the line. These approximations hold 

 for very low frequencies. The second approximation for open and 

 short circuited lines can be obtained with three impedances, as shown 



4 A. E. Kennelly "Artificial Electric Lines, 1917." 

 K. S. Johnson "Transmission Circuits for Telephone Communication, 1925," 

 page 151. 



