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Depending on the movement frequency, outer hair cells can stretch and contract, amplifying the amplitude of the traveling wave at the basilar membrane.

How can they do this exactly? what is the point of the hair cells shortening or stretching?

This question is related to: Sound decomposition of the brain

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    $\begingroup$ It seems you answered your own question? They oscillate in length to amplify the BM motion. What do you mean with how can they do this? Do you mean the biochemical/subcellular processes yielding the motion, or the trigger/neuronal mechanism causing it? $\endgroup$
    – AliceD
    Oct 10 at 18:34
  • $\begingroup$ @AliceD ah i understand - the extension of the cilia of the outer hair cells virtually extends the amplitude of the deflection... sorry i did not imagine this geometrically $\endgroup$
    – Math_Man1
    Oct 13 at 6:42
  • $\begingroup$ No that's not the case. I've answered below. $\endgroup$
    – AliceD
    Oct 13 at 12:27
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Short answer
Outer hair cells physically contract at a rate corresponding to the characteristic resonant frequency at which they are situated on the basilar membrane, thereby mechanically amplifying the basilar membrane movement.

Background
After the exchange of thoughts in the comments I started to understand your question is basically what the mechanism is by which outer hairs cells (OHCs) amplify the basilar membrane (BM) movement.

OHCs can physically oscillate by contracting through an active energy-dependent process. When sound imposes a travelling wave onto the BM, it causes stereocilia deflection on both inner hair cells (IHCs) and OHCs. In both, the mechanical stimulus results in receptor potential changes. In IHCs, these potential changes lead to neurotransmitter release and action potential generation in auditory nerve fibers. In OHCs, by contrast, they result in contraction, which amplifies the BM motion (Fig. 1). Audible sounds in humans go from about 20 Hz to 20,000 Hz. OHCs have been shown to reach contracting rates of up to 70 kHz, meaning they indeed can amplify the BM response along the audible frequency range.

IHCs and OHCs
Fig. 1. IHC and OHC responses in the cochlea. source: University of Minnesota, Dulluth

Reference
- Ashmore, Physiol Rev (2008); 88(1):173-210

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