Tymbal Mechanics and the Control of Song Frequency in the Cicada Cyclochila Australasiae
Authors: Bennet-Clark H. C. 
Published: April 2021

ABSTRACT
The anatomy of the tymbal of Cyclochila australasiae was re-described and the mass of the tymbal plate, ribs and resilin pad was measured.
The four ribs of the tymbal buckle inwards in sequence from posterior to anterior. Sound pulses were produced by pulling the tymbal apodeme to cause the tymbal to buckle inwards. A train of four sound pulses, each corresponding to the inward buckling of one rib, could be produced by each inward pull of the apodeme, followed by a single pulse as the tymbal buckled outwards after the release of the apodeme. Each preparation produced a consistent sequence of pulses.
Each of the pulses produced had its maximum amplitude during the first cycle of vibration. The waveform started with an initial inward-going rarefaction followed by a larger outward compression, followed by an approximately exponential decay, as is typical of a resonant system. The mean dominant frequencies of the pulses produced during the inward movement were 4.37, 4.19, 3.92 and 3.17 kHz respectively. The pulse produced during the outward movement had a mean resonant frequency of 6.54 kHz. This suggests that the mass-to-stiffness ratio that determines the resonant frequencies of the various pulses differs from pulse to pulse.
If succeeding pulses followed rapidly, the next pulse tended to start on the inward-going half-cycle of its predecessor and to produce a coherent waveform. Coherence was lost if the preceding pulse had decayed to below approximately one-tenth of its peak amplitude.
When the tymbal plate was loaded by a 380 μg wire weight, the resonant frequency of all sound pulses was reduced. Pulses produced later in the inward buckling sequence were less affected by the loading than earlier ones. This suggests that the effective mass determining the resonance in the later pulses is greater than that in the earlier pulses. The frequency of the pulses produced in the outward movement was affected most, suggesting that the mass involved was less than that in any of the pulses produced by the inward movement.
The quality factor, Q, of the pulses produced by the inward buckling of the unloaded tymbal was approximately 10. For the outward buckling, Q was approximately 6. The Q of loaded tymbals was higher than than that of unloaded tymbals. The Q of the resonances varied approximately as the reciprocal of the resonant frequency.
Experimental removal of parts of the tymbal showed that the thick dorsal resilin pad was an important elastic determinant of the resonant frequency, but that the mass and elasticity of the tymbal ribs were also determinants of the resonant frequency. The major element of mass is the tymbal plate. The integrity of the tymbal ribs was essential if the buckling movement were to occur.
The force required to cause inward buckling of the tymbal was approximately 0.25 N. The force required to hold the tymbal in the buckled-in position was approximately 0.05 N. This asymmetry in the tymbal compliance, together with the different masses involved in inward and outward buckling, may account for the difference between the resonant frequencies of the inward-going and outward-going clicks.
The tymbal appears to act as an energy storage mechanism that releases energy as the tymbal ribs buckle inwards in sequence. Each pulse provides a large initial impulse to the abdominal resonator, followed by a sustaining resonant vibration at, or close to, the song frequency. Subsequent pulses maintain the coherent resonance of the song pulse.