Bauhaus-Universität Weimar

Titel:
On sound and atmospheric vibrations, with the mathematical elements of music
Person:
Airy, George Biddell
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit38525/185/
MUSICAL STRINGS. 
169 
where 
c‘ = g 
W w 
~L+J 
TV+w 
and the time of a complete vibration, in which sin (et + B) 
goes through all its changes, is 
— = 2tt J 
c V ; 
Ll{W+w) 
g ( Wl+wL ) * 
The time of complete vibration of the first pendulum, 
if not connected with the second, would be 27r A . 
V 9 
Hence the time of vibration is altered, by the connection, 
in the proportion of 1 to ^ • If T be the 
time of complete vibration of the first pendulum, and r 
that of the second, supposed to be unconnected, the 
time of vibration of the first pendulum is altered by 
Wt2 4- WT2 
the connection in the proportion of 1 to ■ 
If, in one combination, the first pendulun 
/A 
T, the connection-alteration is as 1 to * / 
4W + 4wr 
T 
if, in another combination, it vibrates in —, the eon- 
A 
^4 Wt2 + 4 wt' 
nection-alteration is as 1 to 
Hence 
4 Wt2 wT2' 
it appears possible that the frequency of vibration may 
be altered in different proportions for the fundamental 
note and for its harmonics ; and the series of sounds 
which reach the ear may not possess the character of
        

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