Figure 3.

Measured phase speeds at the base (see Fig. 1 for references) are compared with the phase speed predicted for a uniform plate with BM local tonotopic properties (4 mm tonotopic location) coupled to fluid-filled ducts representing scala vestibuli and scala tympani. Model parameters: the boundary condition at the two radial edges of the BM is assumed to be simply supported (clamped does not change the qualitative results, but increases the quantitative phase speeds (not shown)). Fluid and duct properties: ρ = 1000 kg/m³ and c = 1500 m/s, R = 1 mm². BM properties: density accounting for effective additional mass from other Organ of Corti structures is 2000 kg/m³; Young's modulus decreases exponentially from base to apex: E = 1.5e7 (base)–1.55e6 (apex). The hysteretic plate damping factor is 0.05; thickness decreases exponentially from 20 μm (base) to 1 μm (apex); width increases exponentially from 140 μm (base) to 210 μm (apex) and length is 17 mm. BM is assumed to be isotropic for these results; the effect of longitudinal coupling is discussed later.