AUDITORY SENSATIONS 



565 



Thus in the diagram (Fig. 245) 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 component 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 



FIG. 245. d, a compound sound wave, which may be analysed into a, the 

 fundamental tone, and b and c, the first and second overtones. (HENSEN.) 



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 of sounds the resonators devised by 

 Helmholtz are generally employed. These consist of hollow vessels, 

 with an opening at one end, made of different sizes, so that each will 

 resound only to a definite number of vibrations per second. 



BEATS AND DISSONANCE. The overtones of any sound, 

 at any rate the lower ones, are at considerable distance from 

 one another on the musical scale, and therefore differ consider- 

 ably in the number of vibrations of which they are composed. 

 If two tuning-forks be sounded, the vibrations of which differ only 

 by one or two per second, the phenomenon known as ' beats ' is 

 produced. This is due to the summation or interference of the 

 waves from the two tuning-forks. Supposing we have tuning-forks 

 vibrating one at 100 and the other at 101 times a second, and they 

 start vibrating together. At first the waves of compression started 



