THE FREEDOM OF A STRING 289 



Similarly, touching the wire one fourth of its length from 

 an end makes it vibrate in four segments; touching it one 

 fifth of its length makes it vibrate in five segments. 



In the first case, the string vibrated as a whole string and 

 also as two strings of half the length ; hence, three tones 

 must have been given out, one tone due to the entire strings 

 and two tones due to the segments. But we saw in Section 

 267 that halving the length of a string doubles the pitch of 

 the resulting tone, and produces the octave of the original 

 tone; hence a string vibrating as in Figure 183 gives forth 



FlG. 184. When a string vibrates as a whole, it gives out the fundamental note. 



three tones, one of which is the fundamental tone of the 

 string, and two of which are the octave of the fundamental 

 tone. Hence, the vibrating string produces two sensations, 

 that of the fundamental note and of its octave. 



When a string is plucked in the middle without being held, 

 it vibrates simply as a whole (Fig. 184), and gives forth but one 

 note ; this is called the fundamental. If the string is made to 

 vibrate in two parts, it gives forth two notes, the fundamental, 

 and a note one octave higher than the fundamental; this is 

 called the first overtone. When the string is made to move 

 as in Figure 183, three distinct motions are called forth, the 



CL. GEN. SCI. 19 



