508 PHYSIOLOGY 



of sounds the resonators devised by Helmholtz are generally employed. 

 These consist of hollow vessels, with an opening at one end, made of different 



FIG. 247. d, a compound sound wave, which may bo analysed into a, the 

 fundamental tone, and 6 and t, the first and second overtones. (HENSEN.) 



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 considerably 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 by each fork will coincide, so that 

 the total compression of the air at each beat will be the compound effect of 

 the compression produced by the two forks. The two forks therefore will 

 reinforce one another. After the lapse of half a second the tuning-forks will 

 be at different phases of their excursion. The 101 fork will be moving in one 

 direction while the 100 fork is moving in the other, so that the compression 

 produced by one fork coincides with the expansion of the air produced by 

 the moving backwards of the other fork. The sound produced by one fork 

 is therefore diminished by the sound produced by the other fork, and the 

 total sound is less than either of the two forks. At the end of one second, 

 the phases of the two forks once more corresponding, we shall get the sound 

 increased in loudness ; thus there is an alternate waxing and waning of the 

 sound which recurs once a second and is spoken of as a ' beat.' 



The number of beats per second may be used to determine the differences 

 in the vibration frequencies of two forks. Thus two forks vibrating one at 

 100 and the other at 110 will give ten beats per second. As the number of 

 beats increases the effect produced on the ear becomes more and more dis- 



