294: COMPOSITION OF SOUND WAVES. 



(2.) Other conditions being the same, the number of 

 vibrations per second varies directly as the square root of 

 the stretching weight, or tension. 



(3.) Other conditions being the same, the number of 

 vibrations per second varies inversely as the square root of 

 the weight of the string per linear unit. 



(<z.) All of these laws may be roughly illustrated by means of a 

 violin. The length of the string may be altered by fingering ; the 

 tension may be changed by means of the screws or keys ; the effects 

 of the third law may be shown by the aid of the four strings. 



(&.) For the illustration of these laws the sonometer, shown in 

 Fig. 231, is generally used. The length of the string is determined 



FIG. 231. 



by the two fixed bridges, or by one of them and the movable bridge 

 which may be employed for changing the length of the vibrating 

 part of the string ; the tension is regulated by weights, which may 

 be changed at pleasure ; the third law may be verified by using 

 different strings of known weights. Iron and platinum wires of 

 the same diameters are frequently used for this purpose. 



(c.) From these laws it follows, for example, that a string of half 

 the length, or four times the tension, or one-fourth the weight of a 

 given string will vibrate just twice as fast as the given string, i.e., 

 twice as fast on account of any one of these three variations. A 

 string of one-third the length, or nine times the tension, or one- 

 ninth the weight of a given string, will vibrate three times as fast 

 as the given string ; and so on. 



456. The Musical Scale. Starting from any 



