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.
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.
Fig. 1. IHC and OHC responses in the cochlea. source: University of Minnesota, Dulluth
- Ashmore, Physiol Rev (2008); 88(1):173-210