Sharp vibration maximum in the cochlea without wave reflection

The recently discovered sharp vibration maximum of the basilar membrane at the best frequency is difficult to reconcile with the reflectionless traveling wave that is implied by the empirical data. The apparent paradox is resolved by representing the cochlea as a transmission line and investigating its characteristic impedance. The appropriate differential equation has been derived previously (Zwislocki, J. (1953); J. Acoust. Soc. Am. 25, 986-989). It is valid for both long and short wave lengths found in the cochlea. The investigation reveals that, in the presence of sufficiently short waves prevailing around the vibration maximum, the characteristic impedance remains practically constant, independent of the rapid variation of the impedance of the basilar membrane. Since wave reflection depends on variation of the characteristic impedance, no wave reflection should be expected. The constancy of the characteristic impedance also enhances the vibration maximum.