AUDITORY SENSATIONS 507 



If a stretched wire be plucked so as to set it into transverse vibrations 

 will give out a certain note, dependent on its length, its thickness, and the 

 tension to which it is subjected. If its length be halved it will give out a 

 note which is of double the number of vibrations per second. If only one- 

 third of the wire be set into vibrations the sound wave produced will have 

 three times the number of vibrations of that of the whole string. When the 

 string is free to vibrate as a whole the segments of it tend to vibrate even 

 while the whole string is vibrating. If therefore we take the note given out 

 by the whole string, the ' fundamental tone,' as corresponding to 132 vibra- 

 tions per second, there will also be a series of notes'superadded to the funda- 

 mental tone with vibrations per second in the ratio of 1, 2, 3, 4, 5, and 6, &c. 

 Thus if the fundamental tone be c, the overtones, or harmonics, will be 

 produced as is shown below : 





4 5 6 7 8 9 10 



VIBRATIONS PER SECOND 



132 2x132 3x132 4x132 5x132 6x132 7x132 8x132 9x132 10x132 



Nearly all musical instruments, as well as the apparatus for producing 

 the human voice, resemble a stretched wire in giving out overtones in 

 addition to the fundamental tones, and the difference in the quality of 

 various instruments is chiefly determined by the varying predominance 

 of the different overtones. In some the higher overtones may be most 

 marked, in others only the lower overtones. The tuning-fork is practically 

 the only instrument the note of which is pure, i.e. free from harmonics or 

 overtones. It must be remembered that these different tones arrive at the 

 external ear simultaneously. We do not have some particles of air vibrating 

 at one rate and other particles at another rate, but all the simple vibrations 

 of which the component tone is composed are combined together to form a 

 compound wave, the shape of which differs according to the constituent 

 vibrations of which it is made up. 



Thus in the diagram (Fig. 247) the wave shown by the continuous line 

 is compounded of the series of simple vibrations represented by the different 

 dotted lines. The components of such a compound curve can be detected 

 if the sound be analysed by allowing it to act on resonators, i.e. on instruments 

 which can be set into vibration by certain simple tones of which the com- 

 ponent tone is made up. The stretched strings of a piano may be used as 

 a battery of such resonators. If the dampers of the strings be raised, by 

 depressing the loud pedal, and a note be then sounded into the piano, it may 

 be noticed that the piano gives back the sound, and on attaching pieces of 

 straw to the various strings it will be seen that only certain straws vibrate, 

 i.e. those on the strings which are vibrating to the fundamental tone or 

 overtones contained in the sound received by the piano. For the analysis 



