This paper draws attention to symmetric Lloyd-Redwood (SLR) waves-known in ultrasonics as "squirting" waves-and points out that their distinctive properties make them well-suited for carrying positive feedback between rows of outer hair cells. This could result in standing-wave resonance-in essence a narrow-band cochlear amplifier. Based on known physical properties of the cochlea, such an amplifier can be readily tuned to match the full 10-octave range of human hearing. SLR waves propagate in a thin liquid layer enclosed between two thin compliant plates or a single such plate and a rigid wall, conditions found in the subtectorial space of the cochlea, and rely on the mass of the inter-plate fluid interacting with the stiffness of the plates to provide low phase velocity and high dispersion. The first property means SLR wavelengths can be as short as the distance between rows of outer hair cells, allowing standing wave formation; the second permits wide-range tuning using only an order-of-magnitude variation in cochlear physical properties, most importantly the inter-row spacing. Viscous drag at the two surfaces potentially limits SLR wave propagation at low frequencies, but this can perhaps be overcome by invoking hydrophobic effects.