1918] on Vibrations: Mechanical, iVIusical, and Electrical 258 



pitch between. (This was demonstrated on a euphonion kindly 

 lent by Messrs. Boosey & Co.) 



The low " F " is also possible on the bombardon. Both these 

 instruments are characterised by large conical tubing, and the low 

 " F " is obtained by the spread resonance of the sharpened pedal. 



In the case of the trumpet, cornet and French horn with much 

 narrow tubing, the pedals are flattened, so that a pedal of true pitch 

 can only be obtained by the spread resonance, and the " F "' is 

 impossible. On the trombone, which has much small parallel tubing, 

 the low " F " may be obtained occasionally by the downward spread 

 resonance of the second partial (or note number iwo), which is an 

 octave above the pedal. (Demonstration.) The pitch of the notes 

 which have been obtained on six types of instruments by four ex- 

 perimenters are shown in Table J I. 



YI. — MoNOCHORD Vibrations. 



Consideration was next given to the vibrations of stringed instru- 

 ments, beginning with the monochord, because of its striking sim- 

 plicity. 



From the work of mathematicians (with a little help from 

 ex|)eriment) the various possible vibrations of strings, whether 

 plucked, struck or bowed, have long been well known. But a little 

 reflection will show that many other problems are still left con- 

 fronting the physicist. For identical strings excited in the same 

 way, but mounted on different instruments, will produce very 

 diiterent effects on the ear. In other words, the worth of a violin 

 does not lie in its strings, but in its sound-box. 



This leads to the inquiry as to what happens to modify the 

 vibrations as, passing from the strings, they reach in turn the bridge, 

 the belly (or sound-board) and the adjacent air. 



It is easy to see that this problem is somewhat complicated, since 

 it presents so large a number of variables. Thus, there lie at the 

 experimenter's disposal the pitch of the string, its material and 

 dimensions, fhe place and manner of excitation, the material and 

 disposition of the associated parts of the instrument, the place of 

 observing the belly, the portion of the bridge observed and the 

 directions of its motions, and, lastly, the spot at which the motion of 

 the air is observed. In this way a scheme for over a thousand 

 observations could be sketched, even for an instrument with but one 

 string. 



Hence no exhaustive treatment of the problem can be quickly 

 obtained. But a beginning has been made, and by very simple means. 



In a series of experiments simultaneous records have been photo- 

 graphically obtained of the vibrations of the string and of some 

 other part of the instrument. The monochord was placed on a 

 table and light from a vertical slit was focused upon the string near 



