Review of Recent Mathematical Theories of Cochlear Dynamics

An analysis of several theories of cochlear mechanics has been attempted on the basis of general hydrodynamic theory. The theories are divided into two classes according to the mathematical treatment. The first 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 one differential equation when the emphasis put on different factors. The second 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.