the Pianoforte Bridges. 1 1 5 



from the string, this is contrary to all experience, and a little 

 consideration will show that the vibration o£ the string may 

 be transmitted to the sound-board in two other ways. 



(2) Suppose the bridge to be capable of a small movement 

 in a direction parallel to the string and to have a frequency 

 double that of the string ; then it is possible to imagine the 

 sound-board set in vibration by this movement of the bridge 

 and to move towards the string on one downward motion of 

 the bridge and away from the string on the second motion 

 of the bridge, and thus the frequency of the sound-board 

 would be in agreement with that of the string. (Melde's 

 experiments with tuning-forks and strings will occur to the 

 reader.) If the sound-board and string were flat, any such 

 motion of the bridge would mean a corresponding extension 

 of the material of the sound-board and back-wire, and, con- 

 sidering the high elasticity of pianoforte steel wire, whatever 

 motion was possible would be exceedingly small. In practice, 

 the sound-board is always curved like the belly of the violin 

 and the string always passes at less than a right-angle over 

 the edge of the free bridge. Leaving this movement of the 

 bridge for the moment, let us consider the third way in which 

 the sound-board may be set in vibration. 



(3) The string, as it vibrates, not only has a tendency to 

 pull the bridge down parallel to itself but it presses and 

 pulls the bridge during each vibration in a direction at right- 

 angles to the string, thus setting bridge and sound-board in 

 vibration with a frequency the same as that of the string, 

 and also the two halves of the sound-board will be in phase 

 with one another. 



A movement of the bridge and sound-board at right-angles 

 to the string will increase or lower the tension in the back- 

 wire, and when the tension is lowered will allow the bridge 

 to move down slightly, parallel to the string, and in this 

 way a vibration of the sound-board set up as in (2) above 

 is made possible. 



Experiments on Monochord. 



The following experiments were carried out on a monochord 

 constructed as shown in fig. 1. The string used was 99 cm. 

 long and was heavily spun with copper. It was taken 

 from the last note on a pianoforte and was tuned to B n 

 (31 vbns/sec). The sound-board was 15 cm. wide, 0*7 cm. 

 thick, and 86 cm. between the fillets. The sound-bar was 

 2 # cm. thick and 2*16 cm. wide. The bridge was at the 

 middle of the sound-board. 



The resistance offered by the free bridge to a horizontal 



I 2 



