﻿936 On Transverse Vibrations of a String. 



was driven in unison with the fork, and the string was given 

 a small free vibration of the same amplitude as that which 

 had been maintained by the fork. On examining this 

 through the disk, it was found to be giving perceptible beats 

 with the fork. Thus a string with the same amplitude could 

 vibrate with two different frequencies : it seems that the 

 vibration of the string is not merely a maintained vibration 

 with an accommodated pitch, but is to some extent a forced 

 vibration. At the theoretical length the free vibration gave 

 no beats when examined through the disk. Experiments 

 upon this point are still in progress. 



Conclusion. 



The range of length over which a string can be maintained 

 in vibration by a given fork is so great as to render the 

 ordinary form of Melde's longitudinal experiment useless for 

 the determination of the frequency of a fork. The period 

 of vibration of a string can accommodate itself by adjust- 

 ment of plane as well as by adjustment of amplitude. The 

 length of the string when vibrations of very small amplitude 

 just begin is considerably less than the theoretical length. 

 When the theoretical length is reached the plane of vibra- 

 tions becomes vertical, and this provides a means of making 

 the experiment definite ; with horizontal straight-edge stops 

 the plane is always vertical. When the length is greater 

 than the theoretical length, the amplitude increases until, at 

 a certain length, vibrations are only possible when they 

 exceed a certain critical initial amplitude ; this critical 

 amplitude increases w r ith further increase of length. At a 

 still greater length the reaction upon the fork is very con- 

 siderable indeed. By stroboscopic examination, a string is 

 found to have different periods, for the same amplitude, 

 when free and when maintained ; its maintained vibration 

 must be to some extent a forced vibration. 



The discrepancy between theory and practice was observed 

 by Professor Wilberforce, who thereupon suggested the in- 

 vestigation, and I desire to thank him for the interest which 

 he has shown in the experiments. 



George Holt Physics Laboratory, 

 University of Liverpool. 



