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The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study an acoustic pressure wave scattered by a graded array of subwavelength resonators. Using this approach, the spatial frequency separation properties of such an array can be understood. Our set-up is inspired by the graded structure of cochlear hair cells on the surface of the basilar membrane. We compute the resonant modes of the system and explore the model's ability to decompose incoming signals. We propose a mathematical explanation for phenomena identified with the cochlea's ‘travelling wave’ behaviour and tonotopic frequency map.

A fully coupled subwavelength resonance approach to filtering auditory signals