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BELL SYSTEM TECHNICAL JOURNAL 



The function 



1 



i x — 7^1 \ must be integrated throughout the audi- 



tory-sensation area. This was done by graphical methods as shown 

 in Figs. 14 and 15 with the result that T = 324,000. 



Appendix B 



Let the pressure variation of the air in front of the drum of the 

 ear be designated by bp. Since the pressure of the air in the middle 



W -60 



-40 



-20 20 



Values of a 



Fig. 15 



40 



60 



80 



ear balances the undisturbed outside air pressure this change in 

 pressure multiplied by the effective area of the ear-drum is the only 

 effective force that produces displacements. Let the displacement 

 of the fluid of the cochlea near the oval window be designated by X. 

 If Hookes law held for all the elastic members taking part in the 

 transmission of sound to the inner ear then 



X = kdp (1) 



where k is a constant. 



It would be expected from the anatomy of the ear that Hookes 

 law would start to break down even for small displacements. So 

 in general the relation between the force 8p and the displacement 

 X can be represented by 



X=f(8p) =a +a 1 5p+a 2 (8p¥+a i (8py+ .... (2) 



