REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS .1173 



high-frequency response is independent of the "thickness" of the medium 

 and is directly proportional to the ''width" of the track provided 2ira is 

 interpreted as the width of track on a wire. 



The comparisons which have just been made indicate that if the dimen- 

 sions of a wire and of a tape are suitably related, the two media should give 

 identical response at very high and very low frequencies provided they are 

 equally magnetized. The dimensional requirements are 



7ra2 = 8W, 



2Tca = W, and (49) 



R- a = d 



In order to show how the computed responses compare at intermediate 

 frequencies, numerical calculations have been made for a special case in 

 which equations (49) are satisfied. The case chosen is that of a wire 8 mils 

 in diameter moving at a velocity of 12.56 in./sec. past a reproducing head 

 which is effectively one half mil out of contact with the wire {R — a = 

 0.5(10)"^ in.). By equations (49) the corresponding flat medium is a tape 

 which is 2 mils thick and 25.13 mils wide. The tape is assumed to be moving 

 with a velocity of 12.56 in./sec. past a reproducing head which is also 

 effectively one half mil out of contact (d = 0.5(10)~^ in.). In this case 

 the numerical constants in equations (43) and (44) are equal. That is, 



S-n^av = 4TrWv = 25.6 cm.Vsec. 



and the quantity to be computed and compared for the two cases is 



2^^"^^"2T67; 



The computed curves are shown in Fig. 15 from which it can be seen 

 that they coincide at low and high frequencies as planned and that further- 

 more they differ by no more than 1.5 db in the middle range of frequencies. 



As has been pointed out, equation (43) applies only to the unusual case 

 in which the head completely surrounds the wire. The similarity of the 

 two curves of Fig. 15, however, suggests a way of computing approximately 

 the response to be expected when the wire head makes contact with only a 

 part of the circumference of the wire. It suggests that the computation be 

 carried out as though the wire were a flat medium of suitably chosen dimen- 

 sions. In order to make the high frequency end come out right one would 

 expect that W in equation (44) should be given a value equal to the length 

 of the arc of contact between the wire and the head. To make the low 

 frequency end come out right, 5 must be given a value which makes the 

 cross section area of the tape equal to that of the wire, i.e. such 

 that 8W = 7ra2. 



