VIBRATION OF STRINGS 361 



divided into three vibrating portions, as in fig. 216, 

 with two nodes. The note produced makes three times 

 the number of vibrations of the keynote that is, fnds of 



FIG. 216 ( T V real size}. 



.hose of the octave ; it is the twelfth above the funda- 

 mental tone, or the fifth above the octave. 



If the string is touched at 30 or 90 cm that is, one- 

 fourth of its length from one end, three nodes will be 

 .produced, the string will be divided into four ventral 



FIG. 217 ( real size). 



segments, as shown in fig. 217, and the note will make 

 bur times the number of vibrations made in the same 

 ,ime by the fundamental note, that is, the note is two 

 )ctaves above the key-note. 



In a similar manner, the string may be divided into 

 '), 6, 7, 8, and even 12 ventral segments, but as a result 

 )f the whole we shall find that the number of vibrations 

 is inversely as the length of the vibrating segments ; 

 for five segments the number is five times as great, for 

 ix, six times, &c., as the original number of vibra- 

 jions. The string being 120 cm long, if it has a diameter of 



m and a tension of 15 kgr , its fundamental tone will be 

 ). If divided into varying segments, the notes pro- 

 uced by it will be the following : 



