160 DOS. GUY BARLOW AND H. B. KEENE ON THE ANALYSIS OF SOUND. 
effective in producing appreciable motion when its frequency is less than that of the 
(undamped) galvanometer. The full amplitude of the component is not exhibited by 
the galvanometer unless the component has zero frequency ; if it has half that of the 
galvanometer the amplitude of the motion produced is 80 per cent, of the full value (see 
fig. 15, which shows how the forced amplitude varies with the frequency j) of the force). 
On the other hand, a telephone in the circuit will render audible only those com¬ 
ponents which, are of sufficiently high frequency to excite the diaphragm and the ear. 
If the circuit contains appreciable self-induction the effects of interruption are greatly 
complicated—at least theoretically—and special assumptions as to the conditions which 
hold at “ break ” must be made in order to proceed with the investigation. The general 
effect will be to round off the sharp corners at “ make ” and “ break ” in curve (c) 
(fig. 14) as represented in curve (d). Provided the “ time-constant ” of the circuit is 
small, only the components of high frequency will be seriously modified by self-induc¬ 
tion. The order of frequency affected is 1 -j- (time-constant), or R/L if the circuit has 
resistance R and induction L. (For a Broca galvanometer alone R/L is about 
1200/sec.) 
Actually we are not likely to be greatly concerned with the modification introduced, 
for this would imply that we are using the analysis to determine a component of fre¬ 
quency so high that, on account of ordinary impedance, it already must have undergone 
considerable distortion. We shall, therefore, neglect self-induction and proceed to 
consider certain special types of current. 
Then 
(1) Steady Direct Current, 
y — A, a constant. 
y' = -b (sin nt +/ sin 3 nt + &c.). 
2 7T 
The galvanometer is deflected by A/2. The sound in the telephone is represented by 
the uneven harmonic series of tones with the interruption frequency n as fundamental. 
This is the interrupter note ” ; it is characterised by the wave-form (b) (fig. 14). "When 
n is very low only the numerous high harmonics in the audible region are effective, 
and the sound is well described as a purr. As n is increased the note becomes more 
musical in quality, and its pitch is recognisable. 
(2) S.H. Current, 
y = A sin n x t. 
Putting A sin nj, in place of/(f) in the general equation for y' , this may be written : 
A A 
y' = /—sin n x t -|— {cos (n — n { ) t — cos (n + n j) t + l cos (3 n—n^ t — \ cos (3n + ?q) t 
Zj IT 
+ l cos (5 n—Ui) t — i cos (5n + n,) t+ &c—}. 
