Mode conversion in the cochlea? Robert S. MacKay∗ Mathematics Institute and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, U.K. August 28, 2008 Abstract It is suggested that the frequency selectivity of the ear may be based on the phenomenon of mode conversion rather than critical layer reso- nance. The distinction is explained and supporting evidence discussed. PACS numbers: 43.64.Kc, 43.66.Ba Keywords: Cochlea, travelling wave, mode conversion Running title: Mode conversion in the cochlea ∗Electronic mail:
[email protected] 1 1 Introduction The cochlea is the part of the ear where mechanical vibrations (forced by sound waves in the air) are turned into neural signals. There is a huge literature about it, both experimental and mathematical (for summaries, see Robles & Ruggero, 2001, or Ch.23 of Keener & Sneyd, 1998). There are large differences between the cochleae of different species (especially between mammals, birds and reptiles); in this paper attention is restricted to mammalian and usually human cochleae. Most current explanations for the function of the mammalian cochlea are based on “critical layer resonance”, the build up of wave energy at a frequency-dependent place where the wavelength goes to zero, e.g. Lighthill (1981), Nobili, Mammano & Ashmore (1998), de Boer (1996), Hubbard & Mountain (1996), even if the words and mathematical theory are not always used and it is disputed by some (e.g. the discussion in section VII of Olson, 2001). The goal of this paper is to suggest that critical layer resonance is not the right explanation: rather it might be “mode conversion”, the propagation of a wave to a frequency-dependent place where it turns round and comes back out in another wave mode, the energy density forming a peak at the turning point.