The cochlea not only transduces sound-induced vibration into neural spikes, it also amplifies weak sound to boost its detection. Actuators of this active process are sensory outer hair cells in the organ of Corti, whereas the inner hair cells transduce the resulting motion into electric signals that propagate via the auditory nerve to the brain. However, how the outer hair cells modulate the stimulus to the inner hair cells remains unclear. Here, we combine theoretical modeling and experimental measurements near the cochlear apex to study the way in which length changes of the outer hair cells deform the organ of Corti. We develop a geometry-based kinematic model of the apical organ of Corti that reproduces salient, yet counter-intuitive features of the organ's motion. Our analysis further uncovers a mechanism by which a static length change of the outer hair cells can sensitively tune the signal transmitted to the sensory inner hair cells. When the outer hair cells are in an elongated state, stimulation of inner hair cells is largely inhibited, whereas outer hair cell contraction leads to a substantial enhancement of sound-evoked motion near the hair bundles. This novel mechanism for regulating the sensitivity of the hearing organ applies to the low frequencies that are most important for the perception of speech and music. We suggest that the proposed mechanism might underlie frequency discrimination at low auditory frequencies, as well as our ability to selectively attend auditory signals in noisy surroundings.