586 
16 
q 
; a 2\/sinwZ,C, 
(C, + Cz) coswZyC, + (1 a C2C,Zo)( wZoC, )¢. 
This result has been obtained by Lampson (20). 
The order of magnitude of the various parameters may be compared. 
C, is very small, probably less than 40 x 10°'* farad. C, usually varies 
from 10°* farad to 10°" farad. C, = IC where C is approximately 40 x 107? 
farad per foot and / ranges from 20 feet to 1000 feet. Zp, is the surge im- 
pedance and ranges from 50 to 70 ohms for ordinary microphone cables. The 
range of frequencies w/2m of interest in underwater explosion work extends 
up to several hundred kilocycles, say 3 x 10° cycles per second. 
If the length of the cable J is small, then sinwZ,C,/wZ,C, and 
coswZ,C, may be replaced by unity. In that event 
q F 
a aa a [10] 
C,+ C, + C1 —w C5Z, C,) 
If the terminating capacitance C, is not large, then 
q 
hy 2 SS (11) 
= Cm CFC? 
This value for the output voltage of the line is valid for short 
lines and for terminating capacitances C, that are not too large. 
A comparison of Equations [11] and [9] shows that the effect of a 
large value for C, or for | is to increase the value of E, over that which 
would be obtained from Equation [11]. 
The effect of finite lengths of line can be easily estimated. Sup- 
pose it is desired that the value of E, should vary by no more than 4 per 
cent for a range of frequencies up to 3 x 10° cycles per second; assume that 
C, and C, are approximately equal and that C, is negligible. Then Equation 
[9] can be rewritten 
q 
C,(coswZ oC, + SnwZol) 
0™“c 
For small values of the argument wZ,C, we can write 
2 
coswZ,C, = 1 — (above) 
sin wZ,C, ~ (wZ,C,)* 
pzZ.c ee 6 
