6 : 2/ Neural Mechanisms of Hearing 



109 



which the wave velocity is a function of the frequency. In such a 

 medium, one may have a piling up of the waves to maxima in certain 

 regions. This phenomenon can be observed in the build up and 

 decrease of surface waves on the ocean. It is also a familiar idea used 

 repeatedly in quantum theory. 



The various mathematical analyses of the cochlea, using this type of 

 model, are beyond the scope of this text but should be studied by 

 readers with sufficient mathematical preparation. Bekesy demonstrated 



s 



Dental Dam 



£v\\y.v 

 (a) 



Window 

 Analoq 



v/ ".'.' ' • "::." '.'.'.■, 



Analog of 



Apex of Spiral 



(Helicotrema) 



Vibrator 



(b) 

 Analog of Apex 



Dental Dam 



(c) 



Figure 3. Bekesy's hydrodynamic analog of cochlea, (a) 

 Transverse cross section. This shows two channels separated 

 by dental dam. (b) Longitudinal cross section. This shows 

 increase in width from "window" to "apex." (c) Perspective 

 view. The two end windows as well as the partition are of 

 dental dam. 



that these hydrodynamic waves existed not only in the cochlea but also 

 in simple models which are satisfying substitutes for a mathematical 

 analysis. For the simplest model, he used two rigid walls (microscope 

 slides) resting on a solid surface and covered with dental dam (rubber 

 sheet). A slightly more refined system is shown in Figure 3, where two 

 channels and two windows are included. At low frequencies, the actual 

 motion of the dental dam can be observed. There is a maximum region 

 for each frequency ; this maximum is more or less independent of the 

 shape of the channels and varies only slightly for major changes of the 

 thickness or tension of the elastic membrane or of the dimensions of the 

 channel. It is important that one window be driven and the other free. 

 The model emphasizes the biological utility of the hydrodynamic waves 

 whose maxima do not depend on exact physical dimensions. There is a 

 maximum shearing force across the membrane at the maximum in 



