1148 the bell system technical journal, october 1951 



Implications of the Experiment 



In this section it will be assumed that equation (1) holds true in all cases 

 where the spacing d is sufficiently small and the recorded track is sufficiently 

 wide so that end effects are negligible. If this is true, as it seems experi- 

 mentally to be, then it is indeed surprising how great can be the effect of 

 even a very small spacing when the recorded wavelength is small. For 

 example, take the case of a 7500 cps signal recorded at 7.5 in./sec. in which 

 case the wavelength is 0.001 inch. A particle of dust which separated the 

 tape from the reproducing head by one-thousandth of an inch would de- 

 crease the reproduced level by 55 db. A spacing of 0.0001 inch would pro- 

 duce a quite noticeable 5.5 db effect and even at 0.00001 inch spacing the 

 0.55 db loss would be measurable in a carefully controlled experiment. 



In view of the magnitudes involved, it seems probable that this spacing 

 loss may play a significant role even in cases where the reproducing head 

 is supposed to be in contact with the medium. For example, it has been 

 known for some time that chattering of the tape on the reproducing head 

 or changes in the degree of contact due to imperfect smoothness of the tape 

 can result in amplitude modulation of the reproduced signal and thereby 

 give rise to "modulation noise" or "noise behind the signal." 



With the aid of equation (1) it is possible to estimate the magnitude of 

 the noise provided some assumption is made about the wave form of the 

 modulation. To take a simple case, suppose that the roughness of the tape 

 were such as to sinusoidally modulate the spacing by a very small amount 

 and at a low frequency. The reproduced signal would then be modulated 

 and would contain a sideband on each side of the center frequency. The 

 energy in these two sidebands constitutes the modulation noise in this case. 

 If it is required that this noise be 40 db down on the signal, then one can 

 calculate the maximum permissible excursion of the tape away from the 

 reproducing head. This turns out to be 1.1(10)-^ cm. or about one-sixth of 

 the wavelength of the red cadmium line ! Of course, the one mil wavelength 

 assumed in this example is about as short as is often used and the effect 

 becomes less severe as the wavelength is increased. This is one of the rea- 

 sons that speeds greater than 7.5 in./sec. are used for highest quality 

 reproduction. 



One can also make some rough qualitative inferences about the effect of 

 the thickness of the recording medium on the shape of the response curve. 

 As can be seen from equation (1) or from Fig. 2, low frequencies can be 

 reproduced with very little loss in amplitude in spite of considerable spacing 

 between the reproducing head and the medium while high frequencies (i.e. 

 short wavelengths) may be appreciably attenuated by even 0.0001 inch 



