Lewis E R
J Acoust Soc Am. 1984 Sep;76(3):779-86. doi: 10.1121/1.391301.
Zwislocki's original cochlear model, incorporating axial fluid inertia and shunt basilar-membrane stiffness and viscous resistance, possesses an operating regime not previously emphasized in the literature. Even in the absence of basilar-membrane mass and the consequent critical-layer resonance, this regime provides extraordinarily steep high-frequency rolloff. That rolloff is not associated with a critical frequency at which energy flow velocity goes to zero, but is attributable instead to a combination of two effects; (1) frequency-dependent energy coupling to the basilar-membrane viscous resistance, leading to local attenuation of the traveling wave at a rate (Np/cycle) that is directly proportional to frequency, and (2) wavelength that decreases with increasing frequency, thus increasing the number of cycles per unit length of basilar membrane. This combination leads to local attenuation of the traveling-wave amplitude (hence energy absorption from the traveling wave) that is strongly dependent on frequency, the rate (Np/cm) being proportional to the square of frequency in the long-wave mode. In Ranke's (two-dimensional, short-wave mode) version of the model, the same operating regime leads to attenuation that is even more intensely dependent on frequency, the rate being proportional to the cube of frequency.
兹维兹洛茨基最初的耳蜗模型，纳入了轴向流体惯性以及并联的基底膜刚度和粘性阻力，具有一种文献中此前未强调的工作模式。即便在没有基底膜质量以及随之而来的临界层共振的情况下，这种模式也能提供极为陡峭的高频滚降。那种滚降并非与能量流速度变为零的临界频率相关，而是相反地归因于两种效应的组合：（1）与频率相关的能量耦合至基底膜粘性阻力，导致行波以与频率成正比的速率（奈培/周期）局部衰减，以及（2）波长随频率增加而减小，从而增加了基底膜每单位长度的周期数。这种组合导致行波幅度的局部衰减（从而从行波中吸收能量）强烈依赖于频率，在长波模式下速率（奈培/厘米）与频率的平方成正比。在兰克（二维、短波模式）的模型版本中，相同的工作模式导致衰减对频率的依赖更为强烈，速率与频率的立方成正比。
