﻿a String Maintained by Forces of Double Frequency, 933 



are placed horizontally below the string ; one of the stops 

 is attached to a travelling-microscope table, in order that it 

 may be moved uniformly. The fork is placed on a separate 

 table to prevent direct communication of vibrations. 



If a stroboscopic disk, driven in unison with the fork, be 

 arranged so that the eye looks through slits which are 

 moving along the length of the string, then, on account of 

 phase differences, the string appears to have a series of loops 

 (since its frequency is half that of the fork), the number of 

 loops increasing as the eye is withdrawn farther from the 

 disk : if the slits move at right angles to the string, a series 

 of straight lines are seen. By examining the string through 

 the disk in this manner, and observing the stability of nodes, 

 a knowledge of the condition of the string can be obtained, 

 and the presence of overtones &c. detected. The amplitude 

 of the fork at the point of attachment of the string was 

 measured in the microscope and found to be 0*22 mm. 



The following observations relate to the string vibrating 

 in one segment ; the present note does not include any 

 reference to the results with two or more segments. 



If the stops consist simply of horizontal straight edges, 

 the vibrations of the string are executed always in the 

 vertical plane, this being due to the fact that the stops, if 

 smooth, exert no reactions for horizontal vibrations. With 

 the string resting in the notches, however, the plane of 

 vibration is definite, and depends simply upon the length, 

 whether a given length be approached by shortening or by 

 lengthening the string. If the plane of vibrations be dis- 

 placed from this plane of equilibrium, it returns to it with 

 more or less eagerness, depending upon the length of the 



string. 



The explanation of the mode of action of the string given 

 by Tyndall *, though incorrectly illustrated in his diagram, 

 is well illustrated in the string, every point of which is 

 found to be describing a curve convex towards the fork ; the 

 curvature for points near the fork is greater than for points 

 distant from the fork ; this curvature is, of course, more 

 marked the greater the amplitude of the fork at the point of 

 attachment of the string. 



Starting with the length too short for any vibrations to 

 be produced in the string, if the length be gradually in- 

 creased there will be found a sharply defined point, at which 

 vibrations of very small amplitude will commence ; the 

 plane of these vibrations is usually inclined to the vertical. 



* < Sound,' 2nd ed. p. 105. 



