CHAPTER IX. 

 WAVE ANALYSIS IN REFERENCE TO ACTION IN THE EAR. 



It can 1)6 safely assumed that the vibration in the air is transmitted 

 through the middle ear without any essential change of form to the fluid 

 of the labyrinth. What then occurs is still a matter of conjecture. 



The prevailing hypothesis is the one known as the Helmholtz theory. 

 The fibers of the basilar membrane in the cochlea have different lengths. 

 Each can vibrate independently of its neighbors. A sinusoid vibration 

 arriving in the labyrinth would set in vibration that fiber whose natural 

 period agrees with that of the vibration. The vibration of a fiber arouses 

 the nerve connected with it. If the vibration arriving in the labyrinth 

 has a period to which there is no corresponding fiber, it will arouse the 

 two fibers whose periods are just above and just below it with amplitudes 

 corresponding to its relation to each. When a complex of vibrations 

 reaches the labyrinth, those fibers will respond whose periods correspond 

 to the components of the vibration. " Here we find an explanation why 

 the ear analyzes the vibration of the air into sinusoid vibrations. Any 

 particular particle of air can, of course, at any time perform only one 

 movement. That we consider such movement to be mathematically a 

 sum of sinusoid vibrations is at first an arbitrary fiction introduced for 

 theoretical convenience and without a real meaning. Such a meaning, 

 however, is found for this analysis in the consideration of the laws of 

 resonance, since a periodic movement that is not sinusoid can arouse to 

 resonance bodies of different periods in the harmonic series. We have, 

 however, by our hypothesis reduced the phenomena of hearing to phe- 

 nomena of resonance, and we find therein the reason why an originally 

 merely periodic vibration in the air produces a sum of different sensa- 

 tions, and therefore appears compound for perception."* 



As an analogy we might have several thousand brass resonators tuned 

 to vibration from 16 to 30,000 per second. When a vibration strikes 

 the resonators, that one will respond whose period is the same. If no 

 resonator has the exact period, the two neighboring ones will respond. 

 To find what resonators will respond we have — according to Helmholtz — 

 to perform a harmonic analysis of the vibration. 



♦Helmholtz, Lehre v. d. Tonempfindungen, 5 Aufl., 243, Leipzig, 1896. 



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