68 BELL SYSTEM TECHNICAL JOURNAL 



Similarly if the actual pressure on the ear drum is p, and its effec- 

 tive area, a, the total force on the ear drum pa = D x^- Combining 

 equations (2) and (3) gives 



a M' /Mi Xi 



p'-'^wi^+^y (^) 



or 



^ ^ M a a ^ ^ 



The pressure p is the actual pressure on the ear drum. The 

 pressure p' is that measured and plotted in the diagram. If the walls 

 of the ear canal and the ear drum were unyielding, p and p' would be 

 identical for then M = M' and M^ Xija would vanish. If the yield 

 of the ear canal walls were such as to relieve half the pressure in the 

 canal and that of the ear drum about the same, the difference would be 

 considerably less than one of the divisions, in the diagrams, on the 

 intensity scale. If the drum impedance D should be found to be 

 negligible compared to its load Mi the difference would be consider- 

 able. This, however, is hardly to be expected even through narrow 

 ranges of frequency. If the impedances in the formulas were measured 

 the energy flow into the ear drum could be computed. 



In conclusion, the present status of the ear problem may be sum- 

 marized. The philosophy of external ear dynamics has been touched 

 on but there still remain difficult problems both theoretical and ex- 

 perimental. A start has been made on a sound basis in the explana- 

 tion of the action of the cochlea by Roaf, " Analysis of Sound Waves 

 by the Cochlea," Philosophical Magazine, February 1922. Nothing 

 dependable has as yet been published on the action of the middle 

 ear for audio frequencies. It is usually assumed that the various parts 

 undergo relative displacements at audio frequencies in the same way 

 as they react to static forces but this is very likely far from the truth. 



