Ticking of the clockwork cricket: the role of the escapement mechanism
H. C. Bennet-Clark1,* and
Winston J. Bailey2
1 Department of Zoology, Oxford University, South Parks Road, Oxford OX1 3PS, UK and
2 Department of Zoology, University of Western Australia, Nedlands, WA 6907, Australia
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Fig. 2. (A) Oscillogram of two 3.2 kHz tone bursts, each of four cycles duration. An asymmetric waveform was generated so as to introduce second and third harmonic distortion. (B) Oscillogram to show the effect of electronic filtering by Canary software on the waveform shown in A. Frequencies below 5 kHz were filtered out; an oscillation at this frequency built up before the start of the broad-band waveform and decayed after it had ended. The vertical dotted lines show the beginnings and ends of the two four-cycle tone bursts used as a test signal. (C) Graphs of the cycle-by-cycle frequency of the waveforms in A and B plotted by zero-crossing analysis. The frequencies remained approximately constant within the tone bursts but that of the broad-band waveform fell during the gap between the first and second tone bursts (left-hand scale and filled circles). The frequency of the without-FD waveform (the song pulse after filtering out the peak at the dominant frequency FD of the song pulse) was approximately twice that of the broad-band waveform within the tone bursts (right-hand scale and open circles). Before and after the tone bursts, the plot shows the 5 kHz frequency at which the signal was filtered. The inset shows the convention used to define the phase of a sine wave.
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Fig. 3. The normal song of Gryllus campestris. (A) Oscillogram of a chirp consisting of four pulses of increasing duration and amplitude. (B) Oscillogram of the chirp shown in A after filtering to remove frequencies below 7.5 kHz; this waveform has been amplified 16-fold relative to that in A. A and B use the same time scale. (C) Oscillogram of the fourth pulse of the chirp shown in A on an expanded time scale. (D) Oscillogram of the fourth pulse shown in B after filtering to remove frequencies below 7.5 kHz; this waveform has been amplified 32-fold relative to that shown in (C). (E) Plot of the cycle-by-cycle frequencies of the broad-band waveform shown in C (filled circles) and of the without-FD (the song pulse after filtering out the peak at the dominant frequency FD of the song pulse) waveform shown in D (open circles). The frequency scale for the broad-band waveform is on the left and that for the without-FD waveform is on the right. C, D and E use the same time scale.
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Fig. 4. (A) Oscillogram of the four pulses in a typical chirp of Gryllus campestris. (B) Graph of the cycle-by-cycle frequency against time of five consecutive G. campestris fourth song pulses to show that they are closely similar (thin lines and no data points). In addition, data for pulse 1 from Fig. 3A are superimposed (thick line and open circles).
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Fig. 5. The song of Eugryllodes pipiens. (A) Oscillogram of a single normal pulse within a multiple-pulse sequence. (B) Oscillogram of the pulse shown in A after filtering to remove frequencies below 4.5 kHz; this waveform has been amplified fourfold relative to that shown in A. (C) Plot of the cycle-by-cycle frequencies of the broad-band waveform shown in A (filled circles) and the without-FD waveform (the song pulse after filtering out the peak at the dominant frequency FD of the song pulse) shown in B (open circles); the frequency scale for the broad-band waveform is on the left and that for the without-FD waveform is on the right. A, B and C use the same time scale. D, E and F show 3 ms sections (shown in A, B and C by vertical dotted lines and labels) of the waveforms shown in A and B: D from the start of the pulse, E in the middle of the pulse and F from the end of the pulse. For each, the thick line shows the broad-band waveform and the thin line shows the without-FD waveform, amplified fourfold relative to the broad-band waveform. The time scales in D–F show the regions of the pulse that have been amplified. The vertical dashed lines in D–F show that the relative phasing of the broad-band and without-FD waveforms remains nearly constant throughout the pulse. In F, the decay of the pulse after 21.5 ms is close to exponential with a quality factor (Q) of 23.
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Fig. 6. (A–D) An anomalous pulse from the song of the same Gryllus campestris as in Fig. 3. (A) Oscillogram of a single pulse of a chirp of the song. (B) An oscillogram of the pulse shown in A after filtering to remove frequencies below 7.5 kHz; this waveform has been amplified 16-fold relative to that shown in A. (C) Plot of the cycle-by-cycle frequencies of the broad-band waveform shown in A (filled circles) and the without-FD (the song pulse after filtering out the peak at the dominant frequency FD of the song pulse) waveform shown in B (open circles); the frequency scale for the broad-band waveform is on the left and that for the without-FD waveform is on the right. A, B and C use the same time scale; the asterisks show the regions at which the waveforms and frequency became irregular. (D) A 2.5 ms section of the waveforms shown in A and B from the region around the irregularities in the waveforms. The thick line shows the broad-band waveform and the thin line shows the without-FD waveform amplified 16-fold relative to the broad-band waveform. The time scale in D shows the regions of the pulse that have been amplified, the vertical dashed lines show the relative phasing of the broad-band and without-FD waveforms and the asterisks shows the region of the pulse in which the without-FD waveform became small in amplitude. This was preceded by an irregularity in the broad-band waveform and an increase in amplitude of the without-FD waveform (horizontal dashed lines). (E) Plot of the cycle-by-cycle frequencies of the broad-band waveforms of five pulses that show similar pulse envelopes to that shown in A. The anomaly appears at the same place in each pulse, shown by an asterisk which corresponds with the asterisk in A and B.
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Fig. 7. Anomalous pulse from the song of the same Gryllus campestris as in Fig. 3. (A) Oscillogram of a single pulse of a chirp of the song. (B) An oscillogram of the pulse shown in A after filtering to remove frequencies below 7.5 kHz; this waveform has been amplified 16-fold relative to that shown in A. (C) Plot of the cycle-by-cycle frequencies of the broad-band waveform shown in A (filled circles) and the without-FD (the song pulse after filtering out the peak at the dominant frequency FD of the song pulse) waveform shown in B (open circles). Before 3 ms, both waveforms were very irregular; after 10 ms, the without-FD amplitude became very small. The cycle-by-cycle frequency data in these regions have been deleted. The frequency scale for the broad-band waveform is on the left and that for the without-FD waveform is on the right. A, B and C use the same time scale. The asterisks show the time at which the broad-band waveform started to decay exponentially and the cycle-by-cycle frequency of the broad-band waveform rose by 0.2 kHz, thereafter remaining nearly constant. (D,E) 3 ms sections of the waveforms shown in A and B; D is from the irregular region at the start of the pulse and E is from the region around the irregularities in the waveforms. For both, the thick line shows the broad-band waveform and the thin line shows the without-FD waveform, amplified 16-fold relative to the broad-band waveform. The time scales in D and E show the regions of the pulse shown in A that have been amplified. The vertical dashed lines in D and E show the relative phasing of the broad-band and without-FD waveforms. In D, the box shows the region in which the cycle-by-cycle frequency of the broad-band waveform rose rapidly. In E, the horizontal dashed line shows the region of the pulse in which the without-FD waveform increased and then became small in amplitude; this was associated with the start of the exponential decay of the broad-band waveform. The quality factor (Q) of the exponential decay is shown.
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Fig. 8. A model of the interaction between the file and plectrum of a cricket during sound production. In both A and B, the phase of the interaction between the file and the plectrum during the cycle is referred to the lowest point in the cycle of oscillation of the file, termed 270°. The horizontal arrows show the directions of the closing movements of the two wings. The horizontal dashed lines act as references for the relative positions of the file and plectrum at the moment of impact and the dotted lines show the up-and-down oscillation of the tips of the file teeth. In A, is it assumed that a file tooth is engaged, that an impulse is given throughout the first half-cycle (270–90°) and that the plectrum is detached from the file during the second half-cycle (90–0°). At the start of the next cycle (right-hand side), the plectrum engages with the next file tooth (shown by denser stipple). In B, where the amplitude of oscillation is larger, file teeth are engaged and an impulse is given only during the first one-third of the cycle (270–30°); during the later two-thirds of the cycle, the plectrum is detached from the file (30–270°). Sounds will be produced by the ‘escapement’ at both the impact and release of the plectrum (shown by asterisks in A and C or filled circles in B and C). In A, this will give rise to sounds at multiples of twice the frequency of oscillation and in B to asymmetrical waveforms of the type seen in Fig. 5E. FD is the dominant frequency of the song pulse.
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© The Company of Biologists Ltd 2002
