Review of Recent Mathematical Theories of Cochlear Dynamics

Abstract

An analysis of several theories of cochiear mechanics on the basis of general hydrodynamic theory shows that the theories are divided into 2 classes according to the mathematical treatment. The 1st class assumes that transverse waves propagated along the cochlea are long in comparison to the cross-sectional dimension of the canal. All theories of this class can be deduced from 1 differential equation when the emphasis is put on different factors. The 2d class assumes that the waves are relatively not long, and the mathematical treatment becomes a boundary problem to which no exact solution has yet been found. The analysis of the individual theories indicates a certain convergence of opinions, and it is clear that definite progress has been achieved toward an understanding of the dynamic behavior of the cochlea. In spite of this trend, however, no one of the theories seems entirely satisfactory.