The change in propagation speed means that the long-wave, or one-dimensional, approximation is only valid in the early part of the wave's travel. Near the response peak the wavelength is short enough that energy can flow both down the cochlea and perpendicular to the membrane, so a two-dimensional model is needed. This Mathematica animation shows the pressure wave due to a pure tone as it travels down the cochlea. Darker and lighter regions correspond to pressures above and below the average.
On the left, where the propagation speed is high, the wave in each chamber is essentially one dimensional and the wave travels entirely along the direction of the basilar membrane. As the wave slows down the energy starts to bunch up and there is now a variation in pressure in the direction perpendicular to the length of the cochlea.
After a short distance the energy in the wave is completely dissipated. On the right, very faint waves are actually traveling at an angle, carrying their energy into the basilar membrane where the energy is dissipated in membrane losses.
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