270 ADVANCED ELECTRICITY AND MAGNETISM. 



33. Calculate the exact values of (d) and (e) in problem 32. 

 Ans. (d) 0.00655 joule, and (e) 0.0065 joule. 



Note. The decay of current in a wave on a distortionless line takes place exactly 

 as in an ordinary inductive circuit containing resistance, and the decay of voltage 

 in a wave on a distortionless line takes place exactly as in a condenser that is 

 allowed to stand. See problems 27 and 28. 



34. Two No. 14 B. & S. copper wires are laid 18 inches apart 

 in pure water, and the leakage resistance between wires of 

 one mile of this line is about 10 ohms, (a) Find inductance 



Fig. p33. 



and capacity of the line per mile, the induct! vity of water being 

 90. (b) Find capacity which would have to be added per mile of 

 line (as shown in Fig. 33) to give distortionless transmission. 

 Ans. (a) 0.00408 henry per mile and 0.636 microfarad per mile; 

 (6) 0.857 microfarad. 



35. What fraction of the initial energy of a wave would be 

 delivered to the end of a ten-mile line like that specified in 

 problem 34 with capacity loading sufficient to give distortionless 

 transmission? Ans. 2.i7Xio~ 30 . 



Note. See note to problem 32. 



36. The string in problem 3 is 2 meters long between supports. 

 How many vibrations per second does it make when plucked like 

 a guitar string? Ans. 28.2 complete vibrations per second. 



37. A 2O-mile two-wire line is uniformly charged and set 

 oscillating by closing a switch at one end of the line. What is 

 the frequency of the oscillations? Ans. 2325 cycles per second. 



38. What would be the frequency of the oscillations in problem 

 37 if both ends of the line could be closed at the same instant? 

 Ans. 4650 cycles per second. 



