Quantitative Reappraisal of the Helmholtz-Guyton Resonance Theory of Frequency Tuning in the Cochlea

Figure 2

Geometry of a viscoelastic sheet stretched between parallel rigid supports. Dimensions 𝑥 and 𝑦 represent the axial and radial dimensions of the cochlea, respectively. The unstressed thickness of the sheet is ℎ, and Young’s modulus in the radial dimension is 𝐸. The radial span between supports is denoted 𝑠. A small patch of membrane of cross-section 𝐴=Δ𝑥Δ𝑦 corresponds to a one-dimensional fluid column in Figure 1. The deflection at any point along the span as a function of 𝑥, 𝑦, and time, 𝑡, is denoted 𝑧. Normally 𝑧/𝑠≪1.