|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online December 26, 2008
Journal of Experimental Biology 212, 257-269 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.022731
Mechanical phase shifters for coherent acoustic radiation in the stridulating wings of crickets: the plectrum mechanism
1 School of Biological Sciences, University of Bristol, Woodland Road, Bristol,
BS8 1UG, UK
2 Centre for Ultrasonic Engineering, Department of Electronic and Electrical
Engineering, University of Strathclyde, Royal College Building, 204 George
Street, Glasgow, G1 1XW, UK
3 Department of Biology, University of Toronto at Mississauga, 3359 Mississauga
Road, Mississauga, ON, Canada, L5L 1C6
* Author for correspondence (bzfmz{at}bristol.ac.uk)
Accepted 30 September 2008
 |
Summary |
|---|
 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Key words: biomechanics, stridulation, phase shifter, bioacoustics, Gryllidae, Orthoptera
|
INTRODUCTION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
).
The SF is part of the vein A1, which has developed on the underside
tegminal surface to form a series of teeth. The plectrum is formed by a more
sclerotised projecting part in the tegminal anal region and may also
correspond to a modified anal vein (Figs
1 and
2). The file-bearing tegmen
(FBT) overlaps the plectrum-bearing tegmen (PBT) so that the plectrum moves
and engages with SF teeth on the ventral side of the contralateral tegmen;
hence, the two forewings have adapted to different tasks
(Forrest, 1987). An SF and
plectrum occur in both tegmina, which suggests that crickets can stridulate
using either wing overlapping but males of this family tend to stridulate with
the right tegmen on top (i.e. there is usually a preferred plectrum and a
preferred SF). In crickets, the PBT is the left tegmen
(Fig. 1), which, in most cases,
is overlapped by a right tegmen (also) with a plectrum. In some species,
however, individuals with either tegminal overlapping can be found in equal
proportions (Kavanagh and Young,
1989; Masaki et al.,
1987). In any case, it is not clear whether crickets voluntarily
switch tegminal overlapping during stridulation (the sound produced with
either overlapping is not statistically different) as observed in hump-back
crickets (Morris et al., 2002;
Morris and Gwynne, 1978).
|
|
). The
plectrum is driven across the SF teeth and vibrations produced by SF-plectrum
impacts are amplified by the surrounding wing cells, especially by a
triangular area called the harp (Fig.
1), which resonates at the frequency of tooth impacts
(Nocke, 1971). The motion of
the plectrum over the SF is controlled mostly by the resonant vibration of the
FBT: the passage of a single tooth generates one sound oscillation
(Bennet-Clark and Bailey, 2002;
Elliott and Koch, 1985). This
1:1 correspondence is achieved by an escapement mechanism similar to a clock,
where the harps represent the pendulum and the SF-plectrum represent the
energy supplier (Koch et al.,
1988). The result is a low frequency (range 2–8 kHz)
sinusoidal (tonal) signal, functioning to attract females. This mechanism has
been analysed and discussed in detail in only a few species of Gryllidae and
Gryllotalpidae (Bennet-Clark,
1970; Bennet-Clark,
2003; Bennet-Clark and Bailey,
2002; Koch et al.,
1988; Prestwich et al.,
2000; Prestwich and
O'Sullivan, 2005).
Cricket pure-tone stridulation requires two features: (1) that the main
sound radiators of both tegmina vibrate in phase at the same frequency
[otherwise the output is affected by destructive interference
(Bennet-Clark, 2003)]; and (2)
that the functional file be transversely flexible so as to bend when vibrating
at the resonant frequency (fo) with enough amplitude to
produce catches and releases of the plectrum during every cycle of the
oscillation (Bennet-Clark,
2003; Bennet-Clark and Bailey,
2002; Prestwich and
O'Sullivan, 2005). Additionally, Ensifera species singing below 40
kHz tend to exhibit a systematic distribution of the file teeth: inter-tooth
space gradually increases in the same direction as the plectrum closing
movement (Montealegre-Z,
2005); crickets are not an exception to this rule
(Bennet-Clark, 1987;
Prestwich and O'Sullivan,
2005) (Fig. 3).
Thus, tooth spacing could help to determine the relative velocities of the
tegmina at plectrum–tooth impact
(Koch et al., 1988;
Montealegre-Z and Mason, 2005;
Prestwich and O'Sullivan,
2005), i.e. the tegminal velocity should gradually increase during
the closing stroke.
|
Bennet-Clark analysed the mechanical interaction of the right and left
tegmina in Teleogryllus oceanicus pointing out that the two should be
phase-locked to generate a coherent pulse
(Bennet-Clark, 2003).
Theoretically, when the plectrum engages a file tooth, the tooth and rest of
the FBT moves away from the resting position making a high pressure
(condensation) on its upper face (90 deg. phase), while the plectrum and the
rest of the PBT, receiving the opposite push, would make a low pressure
(rarefaction) on its lower face (270 deg.). Both tegmina would then be
oscillating out of phase by 180 deg. and destructive interference would result
in reduced sound production.
The sinusoidal waveform of the sound pulse, which is built upon the
vibration of both tegmina, does not, however, show discontinuities or lack of
coherence, which suggests that the file-and-plectrum mechanism activates the
sound radiating regions of both tegmina so that they vibrate in phase with
each other. Using probe microphones, Bennet-Clark measured the vibration of
isolated tegmina from different plectrum-wing regions, in response to
vibration generated by a piezo-electric actuator
(Bennet-Clark, 2003). He
observed phase differences between 150 deg. and 210 deg. when the PBT was
driven through the plectrum and through the anal area (see
Fig. 1 for location of this
area). With this, Bennet-Clark
(Bennet-Clark, 2003) provided
evidence that the vibration at the left plectrum can excite a resonance of the
ipsilateral tegmen but that, in so doing, the plectrum acts so that the push
at its edge is converted into an upward movement in the region of the file and
harp. This phase shift explains how the tegmina maintain a proper constructive
phase relationship and make a coherent tonal pulse in crickets.
Although the PBT obviously receives energy through a single region (the plectrum), it is as yet unknown whether the phase of vibration remains uniform in all regions of this tegmen and how energy spreads from the plectrum to the rest of the wing after a tooth impact.
The aim of this paper is to explore the plectrum mechanism in Gryllus
bimaculatus De Greer stridulation in more detail and to test the phase
shifter idea first formulated by Bennet-Clark
(Bennet-Clark, 2003). We
analyse how energy propagates from the plectrum to the rest of the PBT
resonant areas and provide measurements of plectrum and harp motion during
repetitive tooth impacts. Additionally, we propose a new method to study the
mechanism of tegminal stridulation. In contrast to previously used methods, it
does not require removal of the tegmen under experimentation from the
specimen. Instead, the plectrum is stimulated in situ by a real SF
and with tooth impact rates that mimic those used in natural conditions [as
opposed to piezo-transducer stimulation (e.g.
Bennet-Clark, 2003;
Montealegre-Z and Mason,
2005)].
|
MATERIALS AND METHODS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Analysis of pars stridens anatomy
Morphology of the plectrum and of the file tooth distribution was analysed
by scanning electronic microscope (SEM). For the stridulatory file, the right
tegmen was removed from some freshly killed specimens; it was mounted on a
stub and left to dry in a desiccator with silica gel. The detailed anatomy of
the plectrum was studied using transverse sections with a microtome, according
to the process described by Di Sant'Agnese and De Mesy Jensen
(Di Sant'Agnese and De Mesy Jensen,
1984). Microtome sections were mounted on slides and examined in a
light transmission microscope (JEOL, 1200 EX, Tokyo, Japan) at the University
of Bristol. Specimens mounted on stubs were gold-coated and studied by SEM
using a Philips 501B (Netherlands, Eindhoven). SEM images were digitized with
a Keithley DAS 1202 plug-in card (Keithley Instruments, Tauton, MA, USA), and
the software SEM 1.2 (A. Gebert and G. Preiss, Medical School, Lab. of Cell
and Electron Microscopy, Hannover, Germany). For five specimens, we obtained
lateral-view pictures at high magnification of the file that allowed the
accurate determination of tooth depth and inter-tooth distances
(Fig. 3B). Specimens were
scanned and measured twice on two different days. Analysis of the file
morphology was performed on digitised SEM photographs using the dimension tool
of a drawing program (Corel Draw 13, Corel Inc. 2005). Data for a single
specimen represent the average measured from two different sets of SEMs.
Inter-tooth distances were measured from the edge of the cusp of one tooth,
and tooth depth as shown in Fig.
3B. File morphology is described for comparative purposes: as we
describe a new method for in situ wing stimulation, which requires an
excised file mounted on a wheel, it is important to show how file morphology
changes after this procedure.
Recordings of sound
We recorded calling sounds from each male used in the experiment using a
1/8'' condenser microphone Brüel & Kjaer Type 4138, connected to
a Brüel & Kjaer 2633 preamplifier (Brüel & Kjaer,
Nærum, Denmark). The microphone was positioned dorsal to the specimen.
Instantaneous frequency of pulses obtained from sound recordings and pulses
obtained from artificial stimulation (see below), were analysed with the
Zero-crossing module for Canary 1.2.4 software (Cornell University, Laboratory
of Ornithology, Ithaca, NY, USA). Zero-crossing v. 5 was provided by K. N.
Prestwich
(http://www.holycross.edu/departments/biology/kprestwi/ZC/).
Experiments
We induced vibrations of the left tegmen by stimulating its plectrum with
an excised `file as gear' system (referred to here as the `cog-cricket'),
driven by a motor (Fig. 4).
Experimental animals were anesthetised using CO2, then mounted in a
holder affixed with commercial wax (Boxing Wax Sticks, KERR Co., Romulus, MI,
USA), with the left tegmen maintained extended normal to the body
(Fig. 4). The tegmen was
gripped at the hinge (axillary sclerites and folded axillary membranes) with
wax (previous recordings with the micro-scan laser vibrometer showed that in
this region vibrations are low or almost absent, and that the structures
associated with the wing hinge do not resonate at a particular frequency).
This tegmen, by remaining attached to the body and unwounded, retained its
resonant properties unaffected by blood-loss dehydration. The complete
preparation was mounted as shown in Fig.
4B.
|
Mounting a dissected stridulatory file on a plastic ring
The `cog-cricket' machine used a natural SF that was carefully excised from
a teneral specimen and inversely bent and glued around a plastic ring fitted
on the shaft of a motor. This preparation incorporates: (1) a plastic cylinder
LEGOTM (4.8 mm external diameter, 3 mm internal diameter and 4 mm long)
with a thin protruding rib (thickness, 0.6 mm; length, 0.8 mm) extending on
one of the edges (Fig. 4A); (2)
a Mabuchi Motor FA-30RA-2270 (Matsudo, Japan), flat type (length, 25.0 mm;
height, 15.1 mm; diameter, 20.1 mm; shaft size, 9.4 mm; shaft diameter, 2.0
mm) (Fig. 4B). Driven at 1.5 V,
the shaft of the motor rotates with a speed of 9100 rpm but it also ran
smoothly at voltages down to 0.1 V; and (3) a SF removed from the right tegmen
of a teneral male G. bimaculatus. The right tegmina of several newly
moulted males were carefully removed under a dissecting microscope, using
razor blades and No. 5 forceps. Tegmina of recently moulted males were used
because, although teneral, they are flexible enough to tolerate the bending
and gluing processes (see below). Males were separated and kept in individual
cages for approximately five days after their last moult and then the SF
excised from their right tegmen as explained above. The dissected file was
glued to the external rim of the plastic ring
(Fig. 4A).
The SF of crickets is not rectilinear: the anal and proximal parts curve (see Fig. 1), the excised part included only the straightest central file region. A normal SF of G. bimaculatus includes approximately 130–140 teeth and the exclusion of the curved ends left only ca. 70–80 teeth (Fig. 3A shows part of this straight segment). From high-speed video recordings of 13 different males (F.M.-Z, unpublished observations), we observed that sound pulses made by a healthy singing male require hitting 90–105 teeth of the file, the last 10–15 of which occur in the curved proximal region. Therefore, all 70–80 teeth in the excised straight segment of the file mounted on the wheel are part of those normally used during stridulation.
A drop of cyanoacrylate gel superglue (Henkel Loctite, Winsford, Cheshire, UK) was applied to the edge of the ring's rim and was left exposed to the air for a few seconds until it became tacky. Then the dorsal part of the file was gently pressed against the spread glue, pushed down first at one of its ends, then progressively along the rim's circumference. Light pressure was applied until the adhesive completely stabilised (approx. 1 min). Once the file was affixed and shaped to the rim's circumference contour, the excess portions of the rim were removed with a razor blade (Fig. 4A,C); thus only the region bearing the file contacted the plectrum during each cycle of rotation. The length of the retained arc bearing the file was ca. 3.5 mm (Fig. 4A,C). The preparation was left to dry for about 48 h to allow cuticular hardening. A total of two excised files from teneral specimens were used in the experiments incorporated in this paper. The effects of bending the SF on tooth distribution and removing its curved parts are presented in the results.
Unlike actual file teeth, those on our preparation did not deviate from a
straight line; this was necessary because all were required to hit the
plectrum during the rotation of the gear (under natural conditions, several of
the teeth from the curved parts of the file are hit because the tegmina close
at an angle [see fig. 4C in
Bennet-Clark (Bennet-Clark,
2003)]. The process of gluing the SF to a rigid surface will
change its mechanical properties (elasticity, hardness, Poisson's ratio, etc.)
but we are interested here only in the mechanics of the PBT: in other words,
the process of stimulating the plectrum with a damped file can provide
information only on PBT vibration and not on two resonating wing structures
vibrating simultaneously.
The `cog-cricket' system was inserted on the motor shaft (Fig. 4B). The motor was driven at different voltages (from 0.1 to 1.0 V) using a stabilised TTi power supply (EL302, 18V, 3.3A, Thurlby Thandar Instruments Ltd, Cambridgeshire, UK). Voltage resolution was controlled and observed with a Digital multimeter (ISO-TECH IDM93N, RS Components Ltd, Northants, UK) connected between the power supply and the motor. For calibration, the rotational speed of the `cog-cricket' system was measured at different voltages using a high-speed video camera (HSV-500c3, NAC Image Technology, Simi Valley, California, USA), which allowed us to select the range of voltages that generated a tooth-passage rate of 4700–5000 teeth mm–1. This span of appropriate tooth-passage rate was obtained with voltages in the range of ca. 170-190 mV.
Plectrum stimulation with a `cog-cricket' system
With the insect mounted, its left tegmen extended, the areas and density of
points on the tegminal surface to scan by laser Doppler vibrometer were
chosen. The plectrum was then stimulated at different rates of tooth passage.
Practically the motor powering the `cog-cricket' was set into motion, usually
starting at 300–400 mV. The spinning file was carefully positioned close
to the plectrum so that tooth impacts engaged the plectrum ventrally, such
that SF engagements occurred from the anal end toward the costal end, as in a
real closing stroke (Fig. 4C).
The frequency response was monitored in real time with a frequency
analyser.
Although in a singing individual the angle adopted during the closing stroke between PBT and FBT is ca. 15–20 deg. (Fig. 4C), the `cog-cricket' system allowed us to achieve 75–80 deg. This angle was measured against the tangential line that touches the circumference of SF (cog-cricket) rotation at the plectrum contact point (Fig. 4C). The tangential line was traced with a laser pointer mounted on a protractor. A smaller angle of engagement could have been obtained but at angles <75 deg., the ring's rim blocked the beam path of the laser Doppler vibrometer and interfered with proper recording, especially in the plectrum scanned area (see Fig. 4C). However, with an angle of engagement of 20 deg. it is possible to scan most of the harp surface. The harp vibration response to cog-cricket stimulation was recorded, adopting both angles of engagement (20 deg. and 80 deg.) and a constant angular speed. We found no differences in the frequency (paired Wilcoxon test P=0.92; means ± standard deviation: 4.97±0.36 kHz at 20 deg., and 4.95±0.33 at 80 deg., N=6).
The voltage driving the motor was gradually adjusted from an initial
setting (300–400 mV) into the range producing optimal velocities, until
a maximum amplitude peak was observed. At this stage, it was also possible to
appreciate by ear, a reduction in pitch and an increase in the quality of the
output sound as seen in Movie 1 in the supplementary material. This peak
amplitude value was compared with the fo of the tegmen
(obtained by stimulating the wing with periodic chirps, see below), and
experiments were carried out with whichever voltage had provided that
tooth-strike rate. Although the fo of the PBT in crickets
is close to fc of the calling song, the PBT
fo differs among individuals
(Bennet-Clark, 2003). For this
reason, the rotational speed in all experiments was adjusted for every
specimen, until a peak with optimal amplitude, close to the mean
fo, was observed in the fast Fourier Transform (FFT)
analyser windows.
Recordings of tegminal vibrations
Tegminal vibrations were examined in response to sympathetic vibration and
artificial tooth strikes using the `cog-cricket' system. Vibration velocities
were measured by a micro-scanning laser Doppler vibrometer with an OFV-056
scanning head fitted with a close-up attachment; the latter allowed the laser
beam (ca. 5 µm diameter) to be positioned with an accuracy of 1 µm. The
laser spot location on the tegmen membrane was monitored by live video feed to
the vibrometer's controlling computer. The vibrometer allows accurate
measurement of the topography of surface motion in a contact-free way, without
requiring the use of a reflective medium
(Windmill et al., 2007).
For the experiments, we scanned the plectrum and harp area (including the SF and anal vein 2) of the PBT using a lattice of 130–200 measurement points (Fig. 5A). The plectrum area, including a small harp region, was also subsequently scanned at higher resolution using 300–400 measurement points (Fig. 5B). Before the experiments were carried out, tegminal vibrations were examined in the frequency domain in response to acoustic stimulation with periodic (chirp) signals, using a bandwidth of 20 kHz (range 1–20 kHz), 3200 FFT lines and a frequency resolution of 6.25 Hz. The acoustic signals were generated by the PSV 300 internal data acquisition board (National Instruments PCI-4451; Austin, TX, USA), amplified (Sony amplifier model TAFE570; Tokyo, Japan) and passed to a loudspeaker (ESS AMT-1; ESS Laboratory, Inc., Sacramento, CA, USA) positioned 20 cm from the specimen. These recordings allowed us to determine in advance the fo of the tegmen under study, so that for the following experiment (cog-cricket stimulation) the frequency at which a particular tegmen should resonate was known.
|
We recorded sound pressure levels from the `cog-cricket' system on the plectrum, using a 1/8'' condenser microphone Brüel & Kjaer Type 4138 and a Brüel & Kjaer 2633 preamplifier (Brüel & Kjaer). Calibration values provided by the company for gains of 30 and 40 dB were accounted for in the laser vibrometer acquisition settings. In addition to the pressure microphone, a particle velocity microphone was used as a trigger. Particle velocity microphones provide a localised measurement of acoustic radiation and therefore also a reliable trigger signal.
Laser and microphone signals were sampled at rates of up to 204.8 kHz. Measurements resulted from an average of 10–20 measurements at each point and were transformed to the frequency domain using a FFT (rectangular window, frequency resolution, 12.5 Hz).
All experiments were carried out on a vibration isolation table (TMC 784-443-12R; Technical Manufacturing Corp., Peabody, MA, USA) at room temperature (25–27°C) and relative humidity of 50–62%. The vibration isolation table with the specimen and the laser vibrometry measurement head were located in an acoustic isolation chamber (IAC series 1204A; internal dimensions: length, 4.50 m; width, 2.25 m; height, 1.98 m; Industrial Acoustics, Bronx, NY, USA). In synchrony with the mechanical measurements, the microphones were positioned next to the preparation.
Frequency spectra of the laser signal were normalised to those of the
microphone signal by the computation of transfer functions, calculated as the
cross-power spectrum of the laser and the microphone signals divided by the
auto-power spectrum of the latter
(Windmill et al., 2005). The
magnitude-squared coherence between the vibrometer and microphone signals was
also computed for each data point, to assess data quality for the entire
dataset and so estimate the amount of unrelated noise
(Windmill et al., 2007).
Coherence values can range between zero and one, with a value of one
indicating the absence of external, unrelated noise. Data were considered of
sufficient quality when coherence exceeded 85%. From the FFT data, phase
angles were obtained for every point scanned with the laser vibrometer.
Individual resonances of the plectrum and harp
From the tegminal areas scanned shown in
Fig. 5, we selected specific
points to measure local frequency of vibration, individually for the plectrum
(ca. 30 points) and for the harp (ca. 150 points). Frequency was estimated as
the average spectrum from all selected points in each area. The quality
factor, Q, measures a resonant system's internal-to-external damping
and also the rate at which such a system reaches maximum amplitude or decays
(Prestwich and O'Sullivan,
2005). For comparative purposes, Q was measured from
calling song recordings of 11 specimens and from pulses produced by
`cog-cricket' stimulation using the method proposed by Bennet-Clark
(Bennet-Clark, 1999b).
Q was calculated from the free decay of a pulse, i.e. from those
oscillations free from the driving force after plectrum-file disengagement. We
detected that stridulation had ceased using Zero-Crossing analysis. The abrupt
jumps in instantaneous frequency late in the pulses are believed to be
associated with the disengagement of file and plectrum
(Bennet-Clark and Bailey, 2002;
Bennet-Clark, 2003;
Prestwich and O'Sullivan,
2005).
Statistical analysis
From the FFT data, phase angles were obtained for every (single) point
scanned with the laser Doppler vibrometer. For statistical analysis, phase
data were chosen from scanned points aligned in a straight line extended from
the plectrum central region to the harp as shown in
Fig. 1. Before proceeding with
further statistical analysis, phase vectors were normalised with respect to
the lowest phase value for every specimen. From these angular data
representations, a mean vector was calculated trigonometrically by using the
formulae given for grouped data in Batschelet
(Batschelet, 1981). Circular
standard deviation and standard error of mean were also estimated. Plectrum
and harp resonances were compared using a Wilcoxon test for two related
samples. Inter-tooth distances from the SF of five intact males and those of
the two SF used in the experiments (i.e. bent files) were compared in a
two-way analysis of variance (ANOVA). The same test was used for
Q-value comparison. Statistical analyses were carried out using the
program Oriana 2.02e (Kovach-Computing-Services, Anglesey, UK) for circular
statistics and the R software (v. 2.7.1,
www.r-project.org).
Acoustic analyses and plots were generated using Matlab software v. 7.6 (The
MathWorks, Natrick, MA, USA).
|
|
RESULTS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
4.7±0.2 kHz (N=20)
(Fig. 6C). As with most
crickets for which the song has been analysed
(Leroy, 1966;
Simmons and Ritchie, 1996),
pulses present frequency modulation (FM), the fundamental frequency and
overtones fall during the last half of all the song pulses
(Fig. 6B) (see also
Simmons, 1988).
File and plectrum morphology
Fig. 7A shows that tooth
spacing gradually increases (linearly) from the anal to the costal region,
reaching a maximum spacing (40 µm) between teeth numbered 85–90.
Thereafter, the spacing gradually decreases. Tooth-space increments occur in
the same direction as plectrum movement, a common feature in singing
ensiferans that generate pure tones (reviewed by
Montealegre-Z, 2005). Teeth
are also inclined at a 45–47 deg. angle, leaning into the approaching
plectrum (Fig. 3). Individual
tooth morphology in G. bimaculatus is typical of several cricket
species (Walker and Carlysle,
1975): the tooth basal area is small in relation to the cusp area,
the latter being expanded into lateral flaps curved towards the file anal
region (Fig. 3A,B). This tooth
morphology seems to help maximise the plectrum contact region, while at the
same time providing basal flexibility for local bending during file vibration.
The asymmetrical tooth shape and tilted orientation may maximise friction
between plectrum and file, creating an appropriate engagement of both
structures.
|
)].
|
Individual resonances of plectrum and harp
The mean FFT of selected scanned points in either the plectrum or the harp
shows the local frequency of vibration in each area. Both the plectrum and
harp resonate at similar frequency (means ± standard deviation:
plectrum=4.86±0.61 kHz harp=4.91±0.61 kHz; paired Wilcoxon test,
P=0.47, N=24).
Response to SF actuation using the `cog-cricket' system
Using the SF as a gear required bending the dorsal surface of the file onto
the semi-circumference of the ring-rim. After bending, mean inter-tooth
spacing of the SF in two preparations, using files of two different specimens,
significantly increased over the intact SF condition [intact SF mean, 0.033
(N=5); bent file, 0.034 (N=2); d.f.=1, F=11.56,
P=0.001). The bending of the file also altered the angle of attack
but tooth spacing preserved the gradually increasing pattern
(Fig. 7B,C).
As expected, the short SF segment (ca. 70 teeth) mounted on the ring's rim, produced a pulse shorter than that of intact individuals (Fig. 9). `Cog-cricket' pulses varied in length between 6 and 15 ms and, in most cases, exhibited build-up followed by free decay. From time-to-time upward FM from ca. 4.5 to ca. 5.0 kHz would appear in the preparation output. With this method, the fo of the PBT (measured with laser vibrometry and microphones) in 14 different individuals was remarkably constant and kept to the range of 4.5 to 5.0 kHz (Fig. 10). The average Q-factor for the PBT, calculated from the free decay of the three outputs (vibration, pressure and particle velocity), remained in the range of 8 to 10.6 (vibration, 10.6±2.7; pressure, 8.2±1.2; particle velocity, 8.6±1.4, N=14), which was significantly lower (d.f.=1, F=21.5, P<0.001) than the Q values calculated from of the species calling song (12.9±3.7, N=11) (Fig. 9).
|
|
156 deg. (Fig.
12A). The plectrum region maintains a phase of vibration around
ca. 20.0 deg. (range between 4.6±2.5 deg. and 52.2±12.9 deg.,
N=14) but after energy moves away from the plectrum region (toward
the harp), the harp adopts a phase of vibration of ca. 167.3 deg. (range
between 151.1±13.7 deg. and 172.0±10.2 deg., angular mean
± standard error of mean, N=14 in both cases). High-resolution
scans of the plectrum area show that this sudden change occurs at the
transition delineated by a large vein (possibly vein A3), which merges with A1
at the anal node area (Fig. 2
and Fig. 13A,B). The wing
vibrates up and down in a cantilever manner from this region
(Fig. 11B), and plectrum and
harp vibrate with significant gain differences, being higher by several orders
of magnitude, for the harp region (Fig.
14B,C).
|
|
|
|
|
DISCUSSION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
In a normal cricket, stridulatory file inter-tooth spacing increases basad,
toward the costal region (Fig.
2A and Fig. 7A).
Because of this systematic change, it is possible to maintain a constant
plectrum-on-tooth strike rate only if the velocity of the closing stroke also
increases appropriately during sound production
(Bennet-Clark, 2003;
Koch et al., 1988;
Prestwich and O'Sullivan,
2005). After placement, the excised files preserve this tooth
density pattern so a potential limitation of our technique is that motor
velocity is constant while inter-tooth spacing gradually increases. Tooth
contact rate is a function of fc. Therefore, gradual drops
in instantaneous frequency [analogous to the Glissando effect
(Bennet-Clark, 2003)] are
expected when using the `cog-cricket' system. Yet FM in most cases was either
very moderate (ca. 500 Hz) or absent from the pulses made with the
`cog-cricket' system. When FM was intermittently observed, instead of
exhibiting the gradual drop in instantaneous frequency, expected for a
constant tooth strike rate and increasing inter-tooth-distance pattern, a
gradual increment was observed (Fig.
9B–D). We have no explanation for this, although it may be
related to minor variations in a motor's rotational speed when driven at low
voltages. Duration and envelope shape of the pulses generated by `cog-cricket'
apparently depend on orientation and forces applied to the gear with respect
to the plectrum: because this was manually controlled, it was difficult to
apply precisely a constant force and orientation during all experiments.
The results reported here show that the wing vibrations produced by the `cog-cricket' method can be monitored with a Doppler laser vibrometer, pressure and/or velocity microphones.
The mechanical phase shifter in the plectrum of crickets
Bennet-Clark (Bennet-Clark,
1970; Bennet-Clark, 1989;
Bennet-Clark, 1999a;
Bennet-Clark, 2003) suggested
that the plectrum and harp (in the PBT) of crickets and mole crickets vibrate
with phase differences. The present paper not only confirms this work but also
identifies the anatomical location of the structures involved in the
phase-shifting mechanism and provides quantitative data that can be used to
explain how this phase shifter works.
Vibrations induced at the plectrum, propagating to the rest of the PBT, experience a series of discontinuities within the medium of propagation, the tegminal cuticle. With changes in geometry come discontinuities in mass, density, thickness, tension and stiffness – features inherent to ensiferan forewings that have evolved to promote effective sound radiation (Fig. 8).
A vibration travelling across a complex heterogeneous medium, as that
exhibited by the plectrum region, will have a particular behaviour in regards
to reflection and transmission, which depends on the material properties of
both regions of the system. One important property is the characteristic
impedance of the material and discontinuities in impedance
(Hirose and Lonngren, 1985).
The characteristic impedance of a material is the product of mass density and
wave speed. Therefore, given the magnitude of the vibration in the plectrum
region and harp (Fig. 14B,C),
one can observe that oscillations travelling in the cricket PBT system
increase in amplitude after crossing the phase shifter region. This is
analogous to an incident wave travelling from a high density (low wave speed)
region towards a low density (high wave speed) region. In this case, part of
the energy will be reflected back from the boundary (the region where density
and impedance abruptly change) and part will be transmitted across the
boundary [pp. 103-108 in Hirose and Lonngren
(Hirose and Lonngren, 1985)]
to the rest of the sound-radiating regions of the PBT, with a gain in
amplitude. Depending upon the mismatch in wave impedance between the two
media, amplitudes of reflected and transmitted waves can be compared to that
of the incident wave (Fletcher,
1992), and the frequency of the vibration can slightly change from
one medium to the other (Hirose and
Lonngren, 1985). Although not being the main purpose of this
paper, our finding of dissimilar amplitudes of vibration between plectrum and
harp (Fig. 14B,C) suggests
that both regions exhibit different impedances and different densities.
Assuming waves travelling across the plectrum can be analogised to those waves
travelling from a high density region towards a low density one, the energy
reflected back from the boundary (vein A3) could induce the release of the
plectrum from a specific tooth. In other words, this energy might make a
significant contribution to the escapement mechanism.
FFT analysis of the scanned wing regions showed that the fo of plectrum and harp are not significantly different (plectrum= 4.86±0.61 kHz and harp=4.91±0.61 kHz). This indicates that the plectrum torsional fo (its angular natural vibration) matches the fo of the whole tegmen and that such torsional fo is critical for making the phase-shifting mechanism work. Interestingly, if the plectrum is stimulated at lower or higher tooth-strike rates, rates different to that of its own fo, tegmen resonance is lost and thus its sound purity (see Movie 1 in supplementary material). The phase relationship observed in Figs 11 and 12 is also lost, therefore, the escapement mechanism is not at work if the tooth strike rate dramatically changes (Montealegre-Z et al. in prep).
Studying wings in isolation, Bennet-Clark showed that for T.
oceanicus both forewings differ in fo, this normally
being higher for the PBT (PBT=4.56 kHz, FBT=4.21 kHz)
(Bennet-Clark, 2003). This
difference appears to be consistent with the subtle morphological asymmetry of
the tegmina (Bennet-Clark,
2003; Simmons and Ritchie,
1996). Similar differences in the fo between
tegmina occur in the katydid Panacanthus pallicornis
(Montealegre-Z and Mason,
2005): the fo is significantly higher for the
PBT (5.1 kHz) than for the FBT (4.3 kHz).
The Q values calculated here from calling songs and from the PBT
stimulated by the `cog-cricket' system are lower than those reported by
Bennet-Clark (Bennet-Clark,
2003) for T. oceanicus and by Nocke
(Nocke, 1971) for G.
camprestris (>20). Perhaps this has to do with our method of
stimulation and with the fact that the tegmina were left attached to the body.
Bennet-Clark (Bennet-Clark,
2003) measured Q values of both tegmina from vibrations
induced by piezo-electric actuators; and his method might provide a more
accurate measurement of tegminal Q values because the structures are
vibrating freely, unengaged. In our experiments, Q values measured
from pulses produced by the `cog-cricket' were lower because the PBT was
engaged to a file as occurs in actual insect stridulation. Indeed, although
Q values measured from sound recordings were statistically
significantly higher (ca. 12.9) than those measured from the pulses produced
by the `cog-cricket' (8.2–10.6), they both can be considered similarly
low when compared with Q values from free tegminal vibration. This
suggests that the `cog-cricket' method provides a reasonable way of tegminal
stimulation.
The difference in fo observed in crickets between the
left and right tegmina [being higher for the PBT
(Bennet-Clark, 2003)] might be
related to an `imperfect' phase inverting mechanism in the PBT. For a complete
phase shift, one expects a dramatic phase change of 180 deg. between plectrum
and resonator. In the present study, changes of only 156 deg. were
observed.
Could this subtle asymmetry be a mechanism that ensures both wings though
vibrating with slightly different frequencies can be phase-locked?
Bennet-Clark (Bennet-Clark,
2003) suggested that the effective vibration frequencies of the
two wings during sound production are due to the effect on their own free
fundamental natural resonance of the stiffness that is added, either to the
left wing by its plectrum and the right file or to the right wing by the left
plectrum (added by the one engaging with the other). Therefore, the slight
imperceptible asymmetry between the left and right tegmina in crickets
(Bennet-Clark, 2003;
Simmons and Ritchie, 1996)
might not require a perfect phase inverting mechanism in the PBT in order to
correct for the difference in fo of both tegmina and thus
reach an single fc value. Additionally, it has been
assumed that after a tooth strike the SF on the FBT will make its first
vibration toward the higher pressure zone (i.e. 90 deg.) but it might be that
this first movement occurs toward a different phase value. Finally, a
limitation inherent to our method – the adopted angle of engagement
between file and plectrum during `cog-cricket' stimulation (75–80 deg.,
Fig. 4C) – might have
also produced this incomplete inversion.
Plectrum mechanics and phase `shifting' in other stridulating Ensifera
Katydids, crickets and haglids all share a common ancestor, haglids being
the group with the most plesiomorphic conditions
(Jost and Shaw, 2006). As
crickets, haglids have bilaterally symmetrical tegmina (subtle symmetry might
be present) and males produce pure-tone signals for intraspecific
communication (Mason, 1996;
Morris et al., 2002;
Spooner, 1973), therefore, the
production of pure-tone signals using bilaterally symmetrical tegmina is
probably a plesiomorphic trait of the ancestors of extant Ensifera.
If the function of a phase-inverting mechanism is to phase-lock the
vibration of two bilaterally symmetrical tegmina, which are then supposed to
oscillate with similar amplitudes at nearly the same frequency, one would
expect katydids, in species where their wings are bilaterally asymmetrical,
not to require a mechanical phase shifter. Morphological tegminal asymmetry in
katydids was presumably a derived feature from a symmetrical ancestor
[inferred from Jost and Shaw (Jost and
Shaw, 2006)]. But synapomorphically, although the stridulating
wings are asymmetrical in katydids, katydids seem to have a mechanical phase
shifter in the PBT (see Bailey,
1970) (reviewed by
Bennet-Clark, 2003).
This situation leaves open several hypotheses: (1) the fact that some
katydid species and crickets both have a phase shifter mechanism in the PBT
suggests that either katydids preserve the plesiomorphic phase shifter,
derived from a forewing-symmetrical ancestor, which is no longer used during
their modern stridulatory behaviour; or (2) that the top-lying tegmen is not
totally mute (as opposed to Bennet-Clark's
(Bennet-Clark, 2003) and
Bailey's (Bailey, 1970)
conclusions.
Significant differences between the amplitude responses of both tegmina
(free vibration) to sympathetic vibration in the katydid Panacanthus
pallicornis have previously been reported
(Montealegre-Z., 2005). The
PBT is ca. 55% higher than the FBT. Therefore, the FBT is not totally silent.
This suggests (at least in P. pallicornis) that the PBT plays most of
the role (in terms of intensity) during sound radiation but also implies that
a phase-lock mechanism might still be required to maintain the proper phase of
vibration between both tegmina and thus consequent sound purity.
Conclusion and future direction
Crickets using an escapement mechanism employ an elaborate mechanical phase
shifter to change the phase with which vibration at the plectrum region
reaches the rest of the PBT. This phase shifter is necessary to phase-lock the
vibration of the left and right tegmina. The mechanism is more complex than
expected because it has to allow for quick mechanical identification of the
FBT phase shifts (produced by the tooth impacts at different regions on a
flexible file) and account for these as well.
Whereas the PBT maintains a constant input phase during a single file sweep, the FBT exhibits a different situation. The plectrum moves along the file of the FBT adding mechanical energy at successive points as it changes position. If a particular location in the main resonating region of the FBT is chosen arbitrarily, it will be seen that the energy input arising with each tooth must travel different distances (along different lines of transmission) to reach that particular locus. In other words, the point of energy input for the file-bearing wing will change continually as the plectrum moves. For energy travelling variable distances to reach and set into vibration any selected area, the times of energy arrivals must also vary and presumably so will the phases of oscillations at that particular region.
If, instead of visualising a single locus, one considers all possible resonating regions of the FBT, an even more complex situation arises. The FBT will experience phase changes as the plectrum continuously moves along the file and successively strikes teeth at different file regions. While the PBT exhibits a constant phase of vibration due to a constant energy input, the FBT will experience changing phases due to a continuously changing tooth-strike region. If this is the situation, how is it that the sequential phase changes in the FBT do not seem to affect the output song produced by most species of crickets, this being usually a precise coherent (simple sinsusoidal) pulse? Answers to this question might help to understand why most katydids, using higher frequencies than crickets, evolved the conspicuous directional asymmetry of their tegmina and why crickets cannot maintain the song purity at tooth strikes rates above the normal range used by most species (2–8 kHz).
LIST OF ABBREVIATIONS
GLOSSARY
).
|
Footnotes |
|---|
Supplementary material available online at http://jeb.biologists.org/cgi/content/full/212/2/257/DC1
|
References |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Bailey, W. J. (1970). The mechanics of
stridulation in bush crickets (Tettigonioidea, Orthoptera). I. Tegminal
generator. J. Exp. Biol.
52,495
-505.
Batschelet, E. (1981). Circular Statistics in Biology (Mathematics in Biology). Burlington, MA, USA: Academic Press Inc.
Bennet-Clark, H. C. (1970). The mechanism and
efficiency of sound production in mole crickets. J. Exp.
Biol. 52,619
-652.
Bennet-Clark, H. C. (1987). The tuned singing
burrow of mole crickets. J. Exp. Biol.
128,383
-409.
Bennet-Clark, H. C. (1999a). Resonators in insect sound production: how insects produce loud pure-tone songs. J. Exp. Biol. 202,3347 -3357.[Abstract]
Bennet-Clark, H. C. (1999b). Which Qs to choose: questions of quality in bioacoustics? Bioacoustics 9,351 -359.
Bennet-Clark, H. C. (2003). Wing resonances in
the Australian field cricket Teleogryllus oceanicus. J.
Exp. Biol. 206,1479
-1496.
Bennet-Clark, H. C. and Bailey, W. J. (2002).
Ticking of the clockwork cricket: the role of the escapement mechanism.
J. Exp. Biol. 205,613
-625.
Desutter-Grandcolas, L. (2003). Phylogeny and the evolution of acoustic communication in extant Ensifera (Insecta, Orthoptera). Zool. Scr. 32,525 -561.[CrossRef]
Di Sant'Agnese, P. A. and De Mesy Jensen, K. L. (1984). Dibasic staining of large epoxy tissue sections and applications to surgical pathology. Am. J. Clin. Pathol. 81,25 -29.[Medline]
Elliott, C. J. H. and Koch, U. T. (1985). The clockwork cricket. Naturwissenschaften 72,150 -153.[CrossRef]
Fletcher, N. H. (1992). Acoustic Systems in Biology. Oxford: Oxford University Press.
Forrest, T. G. (1987). Sinistrality in the southern and tawny mole crickets (Gryllotalpidae, Scapteriscus). Florida Entomologist 70,284 -286.[CrossRef]
Hirose, A. and Lonngren, K. E. (1985).Introduction to Wave Phenomena (Hardcover) . New York, USA: Wiley & Sons, Inc.
Jost, M. C. and Shaw, K. L. (2006). Phylogeny of Ensifera (Hexapoda: Orthoptera) using three ribosomal loci, with implications for the evolution of acoustic communication. Mol. Phylogenet. Evol. 38,510 -530.[CrossRef][Medline]
Kavanagh, M. W. and Young, D. (1989). Bilateral symmetry of sound production in the mole cricket, Gryllotalpa australis. J. Comp. Physiol. A Sens. Neural Behav. Physiol. 166,43 -49.
Koch, U. T., Elliott, C. J. H., Schaffner, K. H. and Kleindienst, H. U. (1988). The mechanics of stridulation of the cricket Gryllus campestris. J. Comp. Physiol. A Sens. Neural Behav. Physiol. 162,213 -223.[CrossRef]
Leroy, Y. (1966). Signaux acoustiques, comportement et systématique de quelques espèces de Gryllidae (Orthoptères, Ensifères). Bull. Biol. Fr. Belg. 100,1 -134.
Masaki, S., Kataoka, M., Shirato, K. and Nakagahara, M. (1987). Evolutionary differentiation of right and left tegmina in crickets. In Evolutionary Biology of Orthopteroid Insects (ed. B. Baccetti), pp. 347-357. England: Ellis Horwood Limited.
Mason, A. C. (1996). Territoriality and the function of song in the primitive acoustic insect Cyphoderris monstrosa (Orthoptera: Haglidae). Anim. Behav. 51,211 -224.[CrossRef]
Montealegre-Z, F. (2005). Biomechanics of musical stridulation in katydids (Orthoptera: Ensifera: Tettigoniidae): an evolutionary approach. Ph.D. dissertation. Department of Zoology, University of Toronto: Toronto. http://www.collectionscanada.gc.ca/thesescanada/s4-230-e.html
Montealegre-Z, F. and Mason, A. C. (2005). The
mechanics of sound production in Panacanthus pallicornis (Orthoptera:
Tettigoniidae: Conocephalinae): the stridulatory motor patterns. J.
Exp. Biol. 208,1219
-1237.
Morris, G. K. and Gwynne, D. T. (1978). Geographical distribution and biological observations of Cyphoderris (Orthoptera: Haglidae) with a description of a new species. Psyche (Stuttg). 85,147 -167.[CrossRef]
Morris, G. K., DeLuca, P. A., Norton, M. and Mason, A. C. (2002). Calling-song function in male haglids (Orthoptera: Haglidae, Cyphoderris). Can. J. Zool. 80,271 -285.[CrossRef]
Nocke, H. (1971). Biophysik der Schallerzeugung durch die Vorderflügel der Grillen. Z. Vergl. Physiol. 74,272 -314.[CrossRef]
Prestwich, K. N. and O'Sullivan, K. (2005).
Simultaneous measurement of metabolic and acoustic power and the efficiency of
sound production in two species of mole crickets (Orthoptera: Gryllotalpidae).
J. Exp. Biol. 208,1495
-1512.
Prestwich, K. N., Lenihan, K. M. and Martin, D. M. (2000). The control of carrier frequency in cricket calls: a refutation of the subalar-tegminal resonance/auditory feedback model. J. Exp. Biol. 203,585 -596.[Abstract]
Sales, G. D. and Pye, J. D. (1974).Ultrasonic communication in animals . London: Chapman and Hall.
Simmons, L. W. (1988). The calling song of the field cricket, Gryllus bimaculatus (Degeer) – constraints on transmission and its role in intermale competition and female choice. Anim. Behav. 36,380 -394.[CrossRef]
Simmons, L. W. and Ritchie, M. G. (1996).
Symmetry in the songs of crickets. Proc. R. Soc. Lond. B. Biol.
Sci. 263,1305
-1311.
Spooner, J. D. (1973). Sound production in Cyphoderris monstrosa (Orthoptera: Prophalangopsidae). Ann. Entomol. Soc. Am. 66, 4-5.
Walker, T. J. and Carlysle, T. C. (1975). Structure of stridulatory file teeth in crickets: taxonomic and acoustic implications (Orthoptera: Gryllidae). Int. J. Insect Morphol. Embryol. 4,151 -158.[CrossRef]
Windmill, J. F. C., Gopfert, M. C. and Robert, D.
(2005). Tympanal travelling waves in migratory locusts.
J. Exp. Biol. 208,157
-168.
Windmill, J. F. C., Fullard, J. H. and Robert, D.
(2007). Mechanics of a `simple' ear: tympanal vibrations in
noctuid moths. J. Exp. Biol.
210,2637
-2648.
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
Related articles in JEB:
This article has been cited by other articles:
|
|
 |
|
  K. Knight CRICKETS SYNCHRONISE WING VIBRATIONS J. Exp. Biol., January 15, 2009; 212(2): i - ii. [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
