﻿934 Mr. J. H. T. Roberts on Transverse Vibrations of 



As the length is increased the amplitude becomes greater, 

 and the plane of vibrations may change gradually. At a 

 certain point, which, however, is not so well defined as the 

 point where small vibrations begin, the plane slowly rotates 

 to the vertical ; for lengths greater than this the plane 

 shows greater and greater preference for the vertical, and 

 the amplitude goes on increasing. At a further point the 

 string is no longer able to start vibrating from its equilibrium 

 condition of straightness, but if it be given a certain initial 

 amplitude, this will immediately develop into a large ampli- 

 tude* If the length be still further increased there comes a 

 time when the fork is unable to support the large amplitudes 

 with which the string vibrates ; the vibrations of the fork 

 are damped down, the amplitude of the string falls in con- 

 sequence^ until it is below the critical value necessary for 

 starting, the string then falls immediately to the straight 

 position, and the fork goes on vibrating vigorously once 

 more. An idea of the lengths at which these effects happen 

 is given by the following table. 



Table I. 



formal tension = 500 grams weight* 



Mass per unit length of string == 0*01347 grm. per cm* 



Amp. of fork at point of attachment of string = 0*22 mm. 



Frequency 



of 



Fork. 



Calculated 

 length 

 (cm.). 



Least length at which 



very small vibrations 



begin (cm.). 



Greatest length at 



which very small 



vibrations can begin 



(cm.), 



320 

 40-0 



42 85 

 49-18 



1887 

 150-9 

 140-8 

 122-7 



181-3 

 1417 



137-1 

 119-4 



195 ! 9 

 156-7 

 146'6 

 127-0 



It will be seen that the frequency of the fork, if unknown, 

 could not be calculated from any of the numbers given in 

 Table I. It was observed, however, that the length when 

 the plane of vibrations began to show a preference for the 

 vertical was always about the theoretical lengthy and this 

 appears to be the only length which bears any easily recog- 

 nized relation to the theoretical length. Some numbers 

 the coincidence of these lengths are given in 



il lustra ting- 

 Table IL 



