ACOUSTICS OF A SMALL AUSTRALIAN BURROWING CRICKET
:
THE CONTROL OF LOW-FREQUENCY PURE-TONE SONGS
W. J. BAILEY1,
H. C. BENNET-CLARK2,* and
N. H. FLETCHER3
1
Department of Zoology, University of Western Australia, Nedlands, WA 6907,
Australia
2
Department of Zoology, University of Oxford, South Parks Road, Oxford OX1
3PS, UK
3
Department of Electronic Materials, Engineering Research School of
Physical Sciences and Engineering, Australian National University, Canberra,
ACT 0200, Australia
*
Author for correspondence (e-mail:
henry.bennet-clark{at}zoo.ox.ac.uk
)
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Fig. 1. Diagram of the singing burrow of Rufocephalus to show the
dimensions and terminology used to describe the burrow. The position of the
insect in the burrow was estimated from the length of antennae that were seen
projecting through the surface hole and the measured dimensions of the insect
(see Table 1,
Table 2).
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Fig. 12. Response of a parallel resonant circuit tuned to 2.9 kHz with a quality
factor Q of 10 (the circuit is shown in the inset to C) when driven
by tone bursts. In A, B, D and E, the measured amplitude of the input varies
by less than ±5% and the cycle-by-cycle frequency of the input varies
by less than ±10 Hz during the tone bursts. For the symbols used in C
and F, see F. (A) Oscillograms of the waveforms of the drive (Input) and
response (Output) to a 40-cycle tone burst at 2.9 kHz. (B) Oscillograms of the
waveforms of the drive (Input) and response (Output) to a 40-cycle tone burst
at 3.2 kHz. (C) Graphs of the cycle-by-cycle frequency of the inputs to (open
symbols) and the outputs from (filled symbols) the resonant circuit shown in
the inset at the two input frequencies, 2.9 and 3.2 kHz. For the 3.2 kHz
drive, note that the amplitude and frequency of the response vary during the
initial 4 ms of the drive and that during the exponential undriven decay at
the end of the response the frequency falls to 2.9 kHz. (D) Oscillograms of
the waveforms of the drive (Input) and response (Output) to a sequence of two
20-cycle tone bursts at 2.9 kHz. (E) Oscillograms of the waveforms of the
drive (Input) and response (Output) to a sequence of two 20-cycle tone bursts
at 3.2 kHz. In D and E, the gap between the two tone bursts was half a
wavelength,  . (F) Graphs of the cycle-by-cycle frequency of the inputs
to (open symbols) and the outputs from (filled symbols) the resonant circuit
shown in the inset to C at the two input frequencies. For the 2.9 kHz drive,
note the rapid fall in amplitude of the response after the gap between the two
tone bursts; for most of the response, the frequency is closely similar to
that of the drive. For the 3.2 kHz drive, note that the amplitude and
frequency of the response vary during the initial 4 ms of the drive and again
after the gap between the two tone bursts; during the exponential undriven
decay at the end of the response, the frequency falls to the 2.9 kHz, to which
the resonant circuit is tuned.
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Fig. 2. Song structure of Rufocephalus. (A,B) Oscillograms of 5 s sections
of the song of two different insects with different trill lengths to show the
basic song structure. (C) Detail (500 ms duration) of the second trill of the
section of song shown in B. (D) Detail (20 ms duration) of the sixth pulse of
the trill shown in C.
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Fig. 3. Consistent song pulses from a single individual Rufocephalus. (A)
Oscillogram of a single song pulse; the next nine pulses in the trill had
closely similar envelopes and duration (cf. the pulses shown in
Fig. 5A) (B) Frequency
versus relative power spectrum of the pulse shown in A, showing the
best frequency (Fc) and second (2H) and third (3H)
harmonics. (C) Detail of the superimposed frequency versus relative
power spectra of 10 consecutive pulses from the same insect to show the small
range in Fc and peak amplitude that was observed; the
broken lines show the frequencies of the highest and lowest
Fc.
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Fig. 4. (A) Oscillogram of a single song pulse of Rufocephalus. (B)
Cycle-by-cycle frequency within the pulse shown in A to show the deviation
from the best frequency, Fc, plotted using zero-crossing
analysis; the varying frequency at the start of the pulse (shown between the
vertical lines) can also be seen in Fig.
5, Fig. 6 and
Fig. 12. The varying frequency
seen after 21 ms is partly due to noise in the recording. The horizontal
dotted line shows Fc within the pulse. (C) Broad-band
frequency versus relative power spectrum of the pulse shown in A. 2H,
second harmonic. (D) Detail of the frequency versus relative power
spectrum shown in B. The FFT bandwidth was set to 10.9 Hz. The solid lines
show the peak power and Fc, and the dashed lines show the
-3 dB level and -3 dB bandwidth, which give a relative bandwidth
Q-3dB of 55.
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Fig. 5. (A) Oscillograms of 10 consecutive song pulses of a single individual of
Rufocephalus to show the variation. Analyses of the pulses enclosed
in boxes are shown in B-D. (B) Instantaneous frequency within the unimodal
pulse 2 and the trimodal pulse 9 shown in A to compare the variation in
frequency. The smooth envelope of pulse 2 is accompanied by slow changes in
the cycle-by-cycle frequency, whereas the rapid changes in amplitude of pulse
9 are accompanied by rapid changes in cycle-by-cycle frequency. For pulse 9,
parts of the analysis of the waveforms between the first and second and the
second and third sub-pulses, where there are very large deviations in
frequency (shown by an asterisk), have been deleted. (C) Frequency
versus relative power spectrum of pulse 2 in A. Note the narrow
bandwidth of the best frequency Fc and of the second and
third harmonics, 2H and 3H. (D) Frequency versus relative power
spectrum of pulse 9 in A. Note the multiple peaks around
Fc and around harmonics 2H and 3H due, in part, to the
rapid irregular modulation in the trimodal pulse.
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Fig. 6. (A) Oscillogram of a single song pulse of Rufocephalus. (B) Detail
of the decay at the end of the pulse shown in A, with the y-axis magnified
five times, to show the exponential decay that is seen in some song pulses and
the quality factor Q, which was calculated from the rate of decay.
(C) Cycle-by-cycle frequency within the pulse shown in A, plotted by
zero-crossing analysis. Note the rapid change in frequency at the start of the
pulse (cf. Fig. 4 and
Fig. 12), that changes in
frequency between 1 and 10ms are associated with rapid changes in the pulse
amplitude and the abrupt increase in frequency during the exponential decay at
the end of the pulse. The erratic cycle-by-cycle frequency that occurs during
the noisy final decay of the pulse (after the dotted line) has been
deleted.
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Fig. 8. Acoustics of a burrow of Rufocephalus. Oscillograms of an 11-cycle
tone burst at 3.27 kHz used to drive the burrow (thick line) and the resonant
response measured 5 mm inside the burrow (thin line). The amplitude of the
internal sound pressure is shown relative to that of the external driving
sound (horizontal dotted line). The quality factor Q of the resonance
of the burrow, measured from the loge(decrement) of the decay of
the response, was 5.7.
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Fig. 7. Oscillogram of a 200 ms region of a song of Rufocephalus. The
short arrows below the trace show the quiet pulses that occur between the loud
song pulses of many recordings. The long arrow above the trace indicates the
pulse that is shown in detail in B and C. (B) Oscillogram on expanded
amplitude and time scales to show the pulse indicated by the arrow in A in
greater detail. (C) Frequency versus relative power spectrum of the
pulse shown by the arrow in A. The best frequency Fc of
this pulse is similar to that of the loud song pulses (shown by the vertical
dotted line) but, because the pulse is brief, the width of the spectral peak
is broader.
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Fig. 9. Songs of the same cricket singing in its own burrow and after transfer to
another burrow. (A) Oscillograms of single song pulses. Upper: singing in its
own burrow. Lower: singing from the burrow used for the tests shown in
Fig. 8. (B) Cycle-by-cycle
frequency within song pulses produced either from the insect's own burrow
(continuous line traces and filled circles) or from the burrow shown in
Fig. 8 (dotted line traces and
open circles). The analyses of the pulses shown in A are shown by circles and
lines, and those of four other pulses are shown by lines. The horizontal
broken line shows the measured resonant frequency of the burrow into which the
cricket was transferred. (C) Frequency versus relative power spectra
for the two song pulses shown in A. The vertical broken lines mark the best
frequencies Fc of the two spectra: in the insect's own
burrow (thick line) and after transfer to the burrow tested in
Fig. 8 (thin line).
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Fig. 10. Graphs of sound pressure and phase in two different models of the burrow of
Rufocephalus. (A) Response of a natural-size plaster cast to an
external sound source at its resonant frequency Fo, 3.72
kHz. Upper: diagram of the model scaled to the distance axis of the graphs
below, showing the points at which measurements were made. Lower: the bottom
horizontal scale shows distance in terms of the wavelength of the driving
sound. Phase is referred to the sound outside the model: there is a 90°
phase lag between the sound outside the model and that in the top chamber (cf.
Fig. 8). (B) Response of a
model approximately three times natural size driven by an internal doublet
sound source at its Fo, 1.06 kHz. Upper: diagram of the
model scaled to the distance axis of the graphs and showing the position of
the doublet source; the terminology for the regions of the burrow follows that
used in Fig. 1. Lower: sound
pressure and phase data obtained either with the surface hole open (open
symbols) or with the hole closed (filled symbols). The bottom horizontal scale
shows distance in terms of the wavelength of the driving sound. Phase is
referred to that at the surface hole of the model.
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Fig. 11. The effect on the resonant frequency, Fo, of a plaster
model burrow of moving a model cricket along the length of the model burrow.
The graph shows resonant frequency versus distance of the `head'
(left) end of the model cricket from the surface hole. The vertical arrows
show the approximate position of the head of a singing cricket in a natural
burrow (cf. Fig. 1), and the
diagram shows the model cricket approximately in the position adopted by a
singing cricket. The model cricket was moved along the length of the model
burrow using a piece of wire, as shown in the diagram.
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Fig. 13. Dimensions and performance of a numerical model of the burrow. (A) Scale
diagram of the model to show the position of the small doublet source in the
top chamber and the planes of discontinuity (A, B, C, D) used to
calculate the acoustics of the model. The dimensions of the model are based on
those of actual burrows (see Table
2). (B) Graphs of sound pressure (solid line) and phase (broken
line) against distance from the surface hole for the model shown in A at a
resonant frequency Fo of 3.25 kHz. Distance along the
burrow is expressed in millimetres (upper scale) or in terms of the sound
wavelength (lower scale). Phase is given relative to that at the plane of the
dipole source. These data can be compared with those obtained with the
physical models shown in Fig.
10. (C) Graph of the relative radiated sound pressure from the
surface hole against frequency for the model shown in A.
Fo is 3.25 kHz with a quality factor Q of 7,
which are closely similar to values measured for actual burrows, physical
models and of the best frequency Fc of the song
(Table 3).
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© The Company of Biologists Ltd 2001
