1172 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



To compare equations (43) and (44), consider first the limiting cases of 

 very long and very short wavelength. As X approaches infinity they re- 

 duce to 



at 



for the wire and 



dt 



= -dW(STv/\)Im cos M 



(45) 



(46) 



for the tape. 



These two expressions are identical provided the cross section area of 

 the wire, (tta^), is the same as that of the recorded track on the tape, {8W). 



-5 

 -10 

 -15 

 -20 

 -25 

 -30 

 -35 

 -40 

 -45 



0.02 



0.1 0.2 0.4 0.6 0.8 1.0 2 4 



FREQUENCY IN KILOCYCLES PER SECOND 



Fig. 15 — Computed responses for wire and tape showing that the responses are very 

 similar provided the dimensions of the wire and tape are suitably related. 



As X approaches zero, the two expressions reduce to 



dt 

 for the wire, and 



Im COS (co/) 



d^ 

 dt 



= -47rt^(l4^)g-'"^'X COS (co/) 



(47) 



(48) 



for the tape. 



Suppose that the reproducing head makes reasonably good contact with the 

 wire so that s/ R/a = 1. In this case equations (47) and (48) are identical 

 provided the circumference of the wire, {lira), is the same as the width of 

 the recorded track on the tape and p)rovided also the effective spacing be- 

 tween reproducing head and medium is the same in the two cases, 

 {d = R — a).\n both cases only a thin surface layer of the recording me- 

 dium is effective in producing high frequency response. For this reason the 



