( 521 ) 
We have also determined the note which the string gave at the 
above tension by calculation. 
For that purpose the string was cut at a and b (fig. 7) whereby 
its length shrunk to 30 cms. The weight of this piece was found 
to be 0,15 grams. 
By substituting in the formula t=^/ P - where t is half the 
period, *> = 0,15 gr, 7=32,5 cms, ^ = 981,2 cms sec-*, .s = 6000gr, 
According to this calculation the string would have a frequency of 
1099 = 549^5 complete vibrations whereas in reality the frequency 
was 511,9 (Ut t ). . 
These numbers agree sufficiently to show with certainty that in 
both cases the fundamental note of the string was heard. The com¬ 
paratively small difference can be explained by assuming that the 
tension of the string was not exactly 6000 grams in consequence of 
the friction of the string on the bridges and of the cord on the 
pulleys. 
From these experiments it appears that in the mixed sound which 
the violin produces the fundamental note produced by the parallel 
motion of the bridge and by the motion imparted to the air directly 
by the string is still present in sufficient intensity to give tjie 
sound the character of the fundamental as far as the pitch is 
concerned. 1 ) ,. _ . A 
It is indeed well known that the fundamental which determines 
the pitch of a composite note may be of smaller intensity than the 
overtones of the mixture, as Helmholtz showed to be the case with 
the piano. *) ... 
We thus know that the sound given by a violin must be ascribed 
to three distinct causes: 
a. a vibration imparted to the air by the string. 
b . a vibration which the roof of the violin acquires from the 
parallel swing of the bridge. 
c. a vibration communicated to the roof by the transverse vibration 
of the bridge. 
The vibration mentioned under a will be left out of account as 
being of little importance. 
~ i ) Compare Rayleigh, “Theory of Sound”, second ed. Vol. I p. 208 and Bartoh 
35 * 
