TRANSMISSION OF SOUND IN THE EAR 493 



The actual presence of overtones can be demonstrated still more clearly 

 by the use of the Helmholtz resonators. These may have different forms. The 

 one shown in Fig. 195 has the form of a hollow sphere, one opening (a) of 

 which ends abruptly, while the other (&) is drawn out funnellike and so shaped 

 as to fit into the ear. The air of such a resonator in conjunction with that of 

 the auditory passage and the eardrum forms an elastic system, which intensifies 

 the fundamental tone of the sphere. Of course, one can have a whole series 

 of resonators adapted to the different tones. If now a certain resonator be 

 placed to the ear and the attention is directed to a sound or series of sounds 

 in which the particular tone of that resonator occurs, this tone will be intensi- 

 fied to so great an extent that it can readily be heard above the others. 



These and other observations which we cannot go into here make it per- 

 fectly certain that the different overtones actually exist in compound tones. 



The following experiment shows di- 

 rectly that the ear also can receive these 

 overtones and is therefore sensitive to each 

 and every simple vibration of this kind. 

 If the tone g of the first octave be struck 

 on the piano and immediately afterwards 

 the tone c of which g is the second over- 

 tone and the attention be directed steadily 

 to </, one can hear it in the tone c, after the 

 g string has ceased vibrating. In the same 

 way one can convince himself that e of 

 the second octave is one of the overtones FIG. 195. Resonator of Helmholtz. 

 of c. Often the overtones become clearer 



as the string ceases to vibrate, for it appears that they die out more slowly 

 than the fundamental tone. 



The ability of the ear to analyze sounds into their constituents is attested 

 by our every-day experiences that we can easily distinguish the individual 

 tones of an organ though only a person musically trained can name them. 



The facts which make it possible for the ear to analyze sound may be 

 summarized briefly as follows. Every movement of the atmosphere which 

 represents a compound of tones can be resolved into a number of simple 

 pendulumlike vibrations, and for each such vibration there is a tone per- 

 ceptible to the ear whose pitch is determined by the vibration frequency of 

 the atmospheric movement (Ohm's law). 



How does the ear accomplish this analysis? Since the endings of the 

 auditory nerve are found in the internal ear, it is plain that analysis of sound 

 must take place there, also that sounds must be transmitted thither without 

 any considerable change. These phenomena will occupy us in the pages imme- 

 diately following. 



2. TRANSMISSION OF SOUND IN THE EAR 



The external and middle ear together constitute merely an apparatus for 

 the transmission of sound, and careful investigation of auditory sensations 

 has shown that this apparatus is able to transmit sound waves to the internal 

 ear without any considerable modification. 



