Reflection of retrograde waves within the cochlea and at the stapes

A number of authors [de Boer and Viergever, Hear. Res. 13, 101-112 (1984); de Boer et al., in Peripheral Auditory Mechanisms (Springer-Verlag, Berlin, 1986); Hear. Res. 23, 1-7 (1986); Viergever, in Auditory Frequency Selectivity (Plenum, New York, 1986), pp. 31-38; Kaernbach et al., J. Acoust. Soc. Am. 81, 408-411 (1987)] have argued that backward-traveling waves, in striking contrast to waves traveling forward towards the helicotrema, suffer appreciable reflection as they move through the basal turns of the cochlea. Such reflection, if present, would have important consequences for understanding the nature and strength of otoacoustic emissions. The apparent asymmetry in reflection of cochlear waves is shown, however, to be an artifact of the boundary condition those authors impose at the stapes: conventional cochlear models are found not to generate reflections of waves traveling in either direction even when the wavelength changes rapidly and the WKB approximation breaks down. Although backward-traveling waves are not reflected by the secular variation of the geometrical and mechanical characteristics of the cochlea, they are reflected when they reach the stapes. The magnitude of that boundary reflection is computed for the cat and shown to be a large, rapidly varying function of frequency.