﻿Harmonic Motions exhibited by a Stretched String. 979 



string. In illustrating a recent lecture the rotating wheel 

 was driven electrically at constant speed. On starting one 

 fork the usual sine curve was shown ; on silencing it and 

 starting the other, three waves for each of the former 

 waves were made visible; and on starting the former again 

 the compound vibration going through its various phases 

 was exhibited, 



The behaviour of the string when viewed without either 

 o£ the aids above mentioned was in itself interesting. The 

 amplitude was sufficiently large to enable one to see the 

 string take the shape of the compounded wave, but as the 

 phase difference between the two vibrations changed rapidly, 

 the visual impression was of a three-peaked curve. One 

 could see also that the phase difference gave rise to two 

 apparent extra strings. The appearance was most marked at 

 the places corresponding to the ventral segments of the 

 string when giving three loops, and gradually disappeared 

 towards the nodes where, of course, that vibration had 

 diminished to zero amplitude. These two apparent strings 

 coincided at the undisplaced position of the string when 

 the view through the stroboscope was as in PI. XYI. fig. 2, 

 and travelled out to the edges of the loops, when the 

 appearance was as in PL XVI. fig. 1. This is clearly to be 

 explained by the fact that in the first case the place of 

 slowest motion is when the string is in its undisplaced con- 

 dition; and in the second, that then the place of slowest 

 motion is when the string is most displaced. 



Sometimes one of the vibrations set up by the tuning- 

 forks took a circular form. In that case the centre of 

 interest shifted from the view through the stroboscope to 

 the motion of a point on the string as seen in the 

 direction of its length. Such a point then exhibited a 

 modified Lissajous' figure, corresponding to the com- 

 position of two vibrations in perpendicular planes in the 

 ratio 3 : 1, with an extra vibration in one plane superposed. 

 This brings me now to discuss 



IT. The composition of two vibrations in perpendicular planes. 



For this it is only necessary to turn one of the forks 

 through 90°, so that the direction of its vibration is horizontal 

 and perpendicular to the string. In using this method, 

 however, there is often a tendency to set up circular motions, 

 and I find that it is much better if the two forks be set 

 upright so that their directions of vibration are in the 

 line of the string. There are at least two advantages in 



3 S 2 



