Located in the forelegs, katydid ears are unique among arthropods in having outer, middle, and inner components, analogous to the mammalian ear. Unlike mammals, sound is received externally via two tympanic membranes in each ear and internally via a narrow ear canal (EC) derived from the respiratory tracheal system. Inside the EC, sound travels slower than in free air, causing temporal and pressure differences between external and internal inputs. The delay was suspected to arise as a consequence of the narrowing EC geometry. If true, a reduction in sound velocity should persist independently of the gas composition in the EC (e.g., air, CO2). Integrating laser Doppler vibrometry, microcomputed tomography, and numerical analysis on precise three-dimensional geometries of each experimental animal EC, we demonstrate that the narrowing radius of the EC is the main factor reducing sound velocity. Both experimental and numerical data also show that sound velocity is reduced further when excess CO2 fills the EC. Likewise, the EC bifurcates at the tympanal level (one branch for each tympanic membrane), creating two additional narrow internal sound paths and imposing different sound velocities for each tympanic membrane. Therefore, external and internal inputs total to four sound paths for each ear (only one for the human ear). Research paths and implication of findings in avian directional hearing are discussed.

Bush-crickets have tympanal ears located in the forelegs. Their ears are elaborated as they have outer, middle and inner ear components. The outer ear comprises an air-filled tube derived from the respiratory trachea, the acoustic trachea (AT), which transfers sound from the prothoracic acoustic spiracle to the internal side of the ear drums in the legs. A key feature of the AT is its capacity to reduce the velocity of sound propagation and alter the acoustic driving forces of the tympanum (the ear drum), producing differences in sound pressure and time between the left and right sides, therefore aiding the directional hearing of the animal. It has been demonstrated experimentally that the tracheal sound transmission generates a gain of approximately 15 dB and a propagation velocity of 255 ms −1 , an approximately 25% reduction from free-field propagation. However the mechanism responsible for this change in sound pressure level and velocity remains elusive. In this study, we investigate the mechanical processes behind the sound pressure gain in the AT by numerically modelling the tracheal acoustic behaviour using the finite element method and real 3D geometries of the tracheae of the bush-cricket Copiphora gorgonensis. Taking into account the thermoviscous acoustic-shell interaction on the propagation of sound, we analyse the effects of the horn-shaped domain, material properties of the tracheal wall and the thermal processes on the change in sound pressure level in the AT. Through the numerical results obtained it is discerned that the tracheal geometry is the main factor contributing to the observed pressure gain. SIGNIFICANCE It has been shown that the bush-cricket ear is unique among insects since it performs similar biophysical mechanics as the mammalian ear, showing outer, middle and inner ear components for sound capturing, impedance conversion and frequency analysis. This research focused on the outer ear using for the first time 3D geometries of the acoustic trachea (AT, bush-cricket ear-canal) and numerical methods to demonstrate the mechanism of passive sound amplification. Numerical results show that the spatial pressure distribution inside the AT is similar to the distribution observed in the ear-canal of mammals. This suggests a case of convergent evolution where a respiratory structure (the trachea) evolved as an exponential horn to amplify and deliver sound pressure waves to a tympanal organ.

Katydid tympana acoustic impedance Katydids (bush-crickets) are endowed with tympanal ears located in their forelegs' tibiae. The tympana are backed by an air-filled tube, the acoustic trachea, which transfers the sound stimulus from a spiracular opening on the thorax to the internal side of the tympanic membranes (TM). In katydids the sound stimulus reaches both the external and internal side of the membranes, and the tympanal vibrations are then transferred to the hearing organ crista acoustica (CA) that contains the fluid-immersed mechanoreceptors. Hence the tympana are principally involved in transmitting and converting airborne sound into fluid vibrations that stimulate the auditory sensilla. Consequently, what is the transmission power to the CA? Are the TM tuned to a certain frequency? To investigate this, the surface normal acoustic impedance of the TM is calculated using finite-element analysis in the katydid Copiphora gorgonensis. From this, the reflectance and transmittance is obtained at the TM. Based on the results obtained in the frequency range 5-40 kHz, it is concluded that the tympana have considerably higher transmission around 23 kHz, corresponding to the dominant frequency of the male pure-tone calling song in this species.

Bush-crickets (or katydids) have sophisticated and ultrasonic ears located in the tibia of their forelegs, with a working mechanism analogous to the mammalian auditory system. Their inner-ears are endowed with an easily accessible hearing organ, the crista acustica (CA), possessing a spatial organisation that allows for different frequencies to be processed at specific graded locations within the structure. Similar to the basilar membrane in the mammalian ear, the CA contains mechanosensory receptors which are activated through the frequency dependent displacement of the CA. While this tonotopical arrangement is generally attributed to the gradual stiffness and mass changes along the hearing organ, the mechanisms behind it have not been analysed in detail. In this study, we take a numerical approach to investigate this mechanism in the Copiphora gorgonensis ear. In addition, we propose and test the effect of the different vibration transmission mechanisms on the displacement of the CA. The investigation was carried out by conducting finite-element analysis on a three-dimensional, idealised geometry of the C. gorgonensis inner-ear, which was based on precise measurements. The numerical results suggested that (i) even the mildest assumptions about stiffness and mass gradients allow for tonotopy to emerge, and (ii) the loading area and location for the transmission of the acoustic vibrations play a major role in the formation of tonotopy.

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