In mammals, hearing is dependent on three canonical processing stages: (i) an eardrum collecting sound, (ii) a middle ear impedance converter, and (iii) a cochlear frequency analyzer. Here, we show that some insects, such as rainforest katydids, possess equivalent biophysical mechanisms for auditory processing. Although katydid ears are among the smallest in all organisms, these ears perform the crucial stage of air-to-liquid impedance conversion and signal amplification, with the use of a distinct tympanal lever system. Further along the chain of hearing, spectral sound analysis is achieved through dispersive wave propagation across a fluid substrate, as in the mammalian cochlea. Thus, two phylogenetically remote organisms, katydids and mammals, have evolved a series of convergent solutions to common biophysical problems, despite their reliance on very different morphological substrates.