356 (hi Discontinuous Wave-Motion. 



is increased from Z/4 to 1/2, the vibration-curve at every 

 point on the string approaches the simple two-step zigzag 

 form, and finally becomes identical with it. 



Two Unequal Discontinuities. 



By setting the axis of rotation of the frame elsewhere than 

 at the point bisecting AB, the case of two unequal discon- 

 tinuous changes of velocity may be realized experimentally. 

 In this case, no line on the velocity-diagram passes through 

 the centre of the string. If the discontinuities cross at the 

 points 1/2 + h, theory shows the vibration-curves for points 

 outside these limits to be four-step zigzags, in wh ch the 

 two lines of small slope are parallel, but the other two lines 

 are not parallel to each other. Between the limits 1/2 + b the 

 vibration-curves are four-step zigzags in which none of the 

 lines are parallel. Tf 6 = 0, the vibration-curves are every- 

 where of a symmetrical type. Otherwise they are everywhere 

 unsymmetrical. The vibration-curves at the points 1/2 ±b 

 consist of only three lines in each period unless b = 0, in 

 which case there are only two. The most interesting forms 

 are those obtained at the centre of the string and those near 

 an end. 



Fig. 2 (Plate VIII.) shows some records obtained when the 

 axis of rotation of the frame passed through a point of tri- 

 section of the length A B. Here again a complete agreement 

 with theory is shown. Forms of vibration set up by two 

 discontinuous changes of velocity may be obtained by bowing 

 a string near one end with pressure insufficient to elicit a 

 pre-eminent fundamental*. In this case the discontinuities 

 are generally unequal, though in special cases they may 

 approach or attain equality. Generally, the vibration-forms 

 thus obtained are unsymmetrical ; but they may closely 

 approximate to the symmetrical types under favourable 

 conditions f . 



Summary and Conclusion. 



By setting up two discontinuous changes of velocity, 

 either simultaneously or in succession, upon a stretched 

 string which has initially a uniform angular velocity, 



* "On the Wolf-note in Bowed Stringed Instruments." Bv C. V. 

 Raman, M.A. Phil. Mag. Oct. 1916. 



* Some of the symmetrical stationary forms with two unequal dis- 

 continuities obtained by bowing- were observed and figured by Hehnholtz 

 (' Sensations of Tone/ English Translation by Ellis, page 85). Helmholtz's 

 drawing is. however, not quite correct, as the snorter descent should 

 appear in the vibration-carve as less steep than the longer. 



