CH. xxx. VTBRA TION CF STRINGS. 267 



two of the riders will fly off, showing that the long end of 

 the string is vibrating, but the one at <, one-third from the 

 end of the string, will remain, showing that at this point the 

 string is comparatively quiet. The long part of the string 

 has, in fact, divided of its own accord into two parts a, b 

 and b, c, each of them of the same length as the one you 

 made with the feather. Thus you have three short strings 

 all vibrating at the same note, and, therefore, all sounding 

 the same note. 



But why should the long end of the string divide itself 

 into two parts ? 



To answer this, take a long cord, and fastening one end 

 of it to the wall, move your hand so as to make it rise up 

 into one great wave-crest, a No. i, Fig. 49. When this wave 



No. 2 



No. 3. 



FIG. 49. 



Vibrating cords showing how nodes are formed. 



In No. 2 the line a, b, c, /, e, represents the shape of the cord during one half of the 

 vibration, and the line a, g, c, d, e, the shape during the other half of the vibration. 



reaches the wall it will be reflected, and will return to your 

 hand, this time not as a crest, but in the shape of a valley 

 or trough, b, and, as the rope is moving very rapidly, this 

 will give the spindle-shaped appearance shown in the figure. 

 Next move your hand more quickly so as to make a 

 crest and a trough, a, b, c, /, e, No. 2, between your hand 



