Mammalian hearing operates on three basic steps: 1) sound capturing, 2) impedance conversion, and 3) frequency analysis. While these canonical steps are vital for acoustic communication and survival in mammals, they are not unique to them. An equivalent mechanism has been described for katydids (Insecta), and it is unique to this group among invertebrates. The katydid inner ear resembles an uncoiled cochlea, and has a length less than 1 mm. Their inner ears contain a hearing organ, crista acustica, which holds tonotopically arranged sensory cells for frequency mapping via travelling waves. The crista acustica is located on a curved triangular surface formed by the dorsal wall of the ear canal. While empirical recordings show tonotopic vibrations in the katydid inner ear for frequency analysis, the biophysical mechanism leading to tonotopy remains elusive due to the small size and complexity of the hearing organ. In this study, robust numerical simulations are developed for an in silico investigation of this process. Simulations are based on the precise katydid inner ear geometry obtained by synchrotron-based micro-computed tomography, and empirically determined inner ear fluid properties for an accurate representation of the underlying mechanism. We demonstrate that the triangular structure below the hearing organ drives the tonotopy and travelling waves in the inner ear, and thus has an equivalent role to the mammalian basilar membrane. This reveals a stronger analogy between the inner ear basic mechanical networks of two organisms with ancient evolutionary differences and independent phylogenetic histories.