Energetics of cicada sound production

Cicadas produce sound by rapid buckling of a pair of domedtymbals situated on the sides of the first abdominal segment(Pringle, 1954). Each tymbal is a highly specialised structurebearing an oval posterior sclerotised tymbal plate, anterior towhich runs a row of narrow vertical ribs of sclerotised cuticle(Fig. 1). These sclerites are separated by and surrounded bystrips of the elastic protein resilin (Weis-Fogh, 1960; Scott,1970; Young and Bennet-Clark, 1995).

During sound production, the posterior tymbal plate is pulledinwards by a large fast muscle (Pringle, 1954; Simmons andYoung, 1978). This tymbal muscle acts as the source of energyin cicada sound production. Each muscle contraction appears toprovide a train of store-then-release cycles of energy to the sound-radiating system via the elastic strain of the tymbal followed bythe release as each tymbal rib buckles. The tymbal muscle hasno muscular antagonist, so re-extension of the muscle is broughtabout by the elastic strain energy in the buckled tymbal.

Initially, the inward movement is opposed by the convextymbal ribs. As the tymbal plate is pulled in further, the tymbal

rib adjacent to it buckles suddenly, becoming concave. Thisrapid buckling movement and the resonant vibration of thetymbal plate produce a pulse of sound. Further contraction ofthe tymbal muscles causes the more anterior ribs to buckle; aseach subsequent rib buckles, a pulse of sound is produced(Simmons and Young, 1978; Young and Bennet-Clark, 1995;Bennet-Clark, 1997). In the Australian cicada Cyclochilaaustralasiae, the tymbal plate plus ribs, in their elasticsurrounds, act respectively as the mass and compliant elementsof a mechanical resonator (Bennet-Clark, 1997).

The vibration frequencies of this resonant system in C.australasiae are close to the dominant frequency of the insect’ssong, so the tymbal acts as major determinant of the songfrequency. The tymbal also acts as a frequency multiplier thatconverts the 117 Hz contraction frequency of each of the pairedtymbal muscles into the 4.3 kHz frequency of the insect’s song(Bennet-Clark, 1997; also see Michelsen, 1983, for a generaldiscussion of the role of frequency multipliers in soundproduction.)

1803The Journal of Experimental Biology 202, 1803–1817 (1999)Printed in Great Britain © The Company of Biologists Limited 1999JEB1998

The anatomy of the paired tymbal muscles of Cyclochilaaustralasiae was described. Force–distance relationships ofthe sound-producing in–out cycle of tymbal movement weremeasured. The largest forces were measured when the pushoccurred at the apodeme pit on the tymbal plate at anglessimilar to the angles of internal pull of the tymbal muscle.

Initially, inward movement was opposed by the elasticityof the tymbal, which stored energy. At a mean force of0.38 N after a mean inward strain of 368 µm, the tymbalribs buckled, the mean energy release being 45.1 µJ. Theenergy release occurred over 2–10 ms in three or foursound-producing steps as successive tymbal ribs buckledinwards. After the ribs had buckled, the force decreased toa mean value of 0.17 N. The force returned to zero duringthe outward movement, during which the tymbal ribsbuckled outwards. The mean energy dissipated in theoutward movement was 32.8 µJ. During contraction, the

tymbal muscle produced mean values for the peak activeforce of 0.31 N over 295 µm, which gave mean values forthe area of the work loops of 47.0 µJ.

The calling song of C. australasiae had a mean pulse rateof 234 Hz (117 Hz for each side of the insect). The peakpower to mean power ratio for the songs was 8.51:1(+9.30 dB). Measurements of the sound field aroundtethered insects and of the peak power to mean power ratioof the songs gave values for the mean power of the song of3.15–7 mW; these correspond to an energy per song pulseof 13.5–30 µJ. Previously reported mean values are3.15 mW for protest song and 5.1 mW for calling song. Theefficiency of transduction of mechanical energy into soundenergy is between 18 and 46 %.

Key words: cicada, Cyclochila australasiae, tymbal, energy storage,transduction, sound radiation.

Summary

Introduction

TRANSDUCTION OF MECHANICAL ENERGY INTO SOUND ENERGY IN THECICADA CYCLOCHILA AUSTRALASIAE

H. C. BENNET-CLARK1,* AND A. G. DAWS2,‡1Department of Zoology, Oxford University, South Parks Road, Oxford OX1 3PS, UK and 2Department of Zoology,

University of Melbourne, Parkville, Victoria 3052, Australia*e-mail: [email protected]

‡Present address: Department of Biological Sciences, Bowling Green State University, Bowling Green, OH 43403, USA

Accepted 31 March; published on WWW 8 June 1999

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In many cicadas, the transduction of sound from mechanicalenergy into acoustic energy takes place in distinct stages.During the first stage, the pulses of sound produced by thetymbals cause high-pressure acoustic vibrations within theabdominal air sac. The abdominal air sac and the large thineardrums of C. australasiae form, respectively, the compliantand inertial elements of a Helmholtz resonator tuned to thesong frequency (Young, 1990; Bennet-Clark and Young,1992). This second stage in the transduction chain maintainsthe purity of the song and assists in producing a smooth songpulse envelope. Because the eardrums are far larger than thetymbals, this second stage also acts as an acoustic impedanceconverter between the tymbals and the surrounding medium(Bennet-Clark and Young, 1992; Bennet-Clark, 1995).

In C. australasiae, the tymbal has four ribs (Fig. 1). As eachrib buckles, it converts a comparatively slow musclecontraction into a brief sound pulse. Each of these sound pulseshas maximum amplitude in the first cycle and thereafter decaysexponentially (Bennet-Clark, 1997). This suggests that thetymbal acts as an energy storage/release mechanism whichprovides an impulse that starts the sympathetic vibration of anabdominal Helmholtz resonator (Young and Bennet-Clark,1995).

The action of the tymbal muscle on the tymbal can bemodelled either by pulling on its apodeme or by pushing on itsinsertion on the tymbal plate (Simmons and Young, 1978;Bennet-Clark, 1997). Previous studies have been concernedwith the nature of the sound produced as the tymbal buckled

and have been essentially qualitative. However, as thetransduction process from muscle power to acoustic power inthis cicada occurs in a comparatively small number of stages,it is feasible to examine the energetics of transduction ofmechanical power to sound power. An earlier attempt to dothis with the mole cricket Gryllotalpa vineae (Bennet-Clark,1970) suffered from uncertainty about the available musclepower, but nonetheless suggested that the efficiency oftransduction was remarkably high.

The insect used here is particularly suitable for energeticstudies of this type. It is large and robust, and the sound isproduced as a long series of similar discrete pulses, each ofwhich is produced by a single muscle contraction, in contrastwith the songs of many other singing insects such as crickets(Popov et al., 1974) or cicadas (e.g. Fonseca, 1991) in whichfar greater inter- and intra-pulse variability occur. Also, manyelements in the sound-producing chain of Cyclochilaaustralasiae have now been studied (Bennet-Clark, 1997;Bennet-Clark and Young, 1992; Josephson and Young, 1981;Young, 1990; Young and Bennet-Clark, 1995).

The present work examines the energetics of various stagesin the sound-production chain of the cicada C. australasiae:the tymbal muscle, the tymbal buckling process and the soundpower that is produced.

Materials and methodsInsects and preparations

Male Cyclochila australasiae Donovan were caught at nightin parkland in Melbourne, Australia, as they emerged from thelast larval instar. Thereafter, they were kept in fine mesh bagson a tree outside the Zoology Department of MelbourneUniversity or on acacia shrubs in the laboratory. In theseregimens, they survived for over 2 weeks. Insects were usedfor experiments between 4 days and 2 weeks after eclosion;only those that produced loud protest song when handled wereused.

For most experiments, insects were prepared by removingthe legs and wings, and then waxing the body to a 6 mmdiameter support rod by the pro- and mesonotum. In addition,for force and distance measurements, the body was made stifferby waxing the first abdominal tergite to the metanotum and thesecond abdominal sternite to the opercula on the thoracicmetasternum using a 5 mm length of femoral cuticle.

Singing was induced by brain stimulation via a pair of0.1 mm diameter stainless-steel insect pins inserted into thefront of the head 2 mm either side of the mid-line and 45 °above the horizontal plane. Sound production was then inducedby short trains of 1 ms duration stimuli at 50 Hz and 2–5 Vamplitude. Insects were mounted head up and, to stretch theabdomen and open the opercula to simulate the position foundin singing insects, a 20 g weight was suspended on a 50 mmlength of wire waxed to the posterior end of the abdomen.

For force measurements on the tymbals, insects were killedby placing them in a freezer at −15 °C for 30 min and thenthawing them immediately prior to use. This procedure

H. C. BENNET-CLARK AND A. G. DAWS

Proberod

Apodemepit

Resilinhinge

Tymbalplate

Anteriorventral

Longribs

Resilinpad

2 mm

Axialpush

Fig. 1. The tymbal of Cyclochila australasiae showing the tymbalplate and the sclerotised tymbal ribs. The drawing shows where theprobe rod of the stiff force transducer (see Fig. 2) was pushed againstthe apodeme pit on the tymbal plate.

1805Energetics of cicada sound production

effectively detached the tymbal muscle from its apodeme andsternal origin and also made it easy to dissect out the tymbalmuscles for weighing.

Tymbal muscle dimensions and trajectory

The area of the tymbal muscle insertion on its apodeme (seeFig. 3C) was measured from camera lucida drawings using aZeiss MOP digital measuring table. Muscle fibre lengths weremeasured directly from the intact insect using Mitutoyo digitalcallipers.

Tymbal muscles were weighed to the nearest 0.1 mg afterdissection from the previously frozen insect. Weighings werecompleted within 5 min of the start of the dissection.

The trajectory of the tymbal muscle fibres was measuredfrom photographs of the abdomen, taken from behind afterremoval of the posterior end or from the mid-line after splittingthe insect’s body along the sagittal plane. The angle of thetymbal muscle apodeme was measured from dissections ofdried specimens.

Force and distance transducers

Because the available commercial force and distancetransducers were unsuitable, special transducers were built,tested and calibrated.

Measurements of the force–distance relationships of thetymbal were made using a stiff transducer with a resonantfrequency of 1 kHz (Fig. 2). The springs were 20 mm lengthsof 12.5 mm wide by 0.15 mm thick stainless-steel shim gluedwith Sylastic silicone rubber to either side of a 12 mm high U-shaped steel support. Two Showa F8 foil strain gauges wereglued with cyanoacrylate adhesive to the central parts of each

of the two outer faces of the steel shims (Fig. 2). These fourstrain gauges were connected as a Wheatstone bridge.

The stiff transducer was used to apply force to the tymbalvia a probe rod glued into one end of the aluminium tubethat connected the springs on either side of the gauge. Ahook for attachment of calibration weights was attached tothe other end of this tube. As the effective mass of the tymbalis less than 1 mg (Bennet-Clark, 1997), the loading of the0.5 g mass of the force transducer by the tymbal wasnegligible. The compliance of this transducer was49 µm N−1, which was approximately one-twentieth of thatof the tymbals. Force could be resolved to 0.01 N at 200 Hzwith linearity and cross-talk from side loads of better than2 %.

The distance moved by the probe rod of the force transducerwas measured using a UGN 3503 linear Hall effect sensorplaced 0.5 mm away from a permanent magnet with a flat face2.5 mm high and 4.5 mm wide glued to the tube that held theprobe rod (Fig. 2). The distance could be measured to ±5 µmover a range of 1 mm. According to the makers’ specification,the bandwidth of the distance sensor was from direct currentto over 10 kHz.

A more compliant force transducer with a resonantfrequency of 100 Hz was constructed for measuring the forceand distance relationships of the tymbal muscle. Itscompliance, 990 µm N−1, was similar to that of a typical cicadatymbal (see Fig. 8). Its sensitivity, its force and distanceresolution and its linearity were similar to those of the stiffertransducer. This compliant transducer was used as an elasticload into which the tymbal muscle contracted; this type ofauxotonic loading has been used to measure the force–distance

Probe rod

Foil strain gauges

Veroboardterminal block

2.3 mm diameteraluminium tube

Hook for calibrationweights

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Silicone rubber

10 mm

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SteelU-shapedsupport

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A B

Fig. 2. Diagrams of the front (A) andside (B) views of the stiff forcetransducer used to measure theforce–distance relationships oftymbal buckling. The constructionand characteristics of this transducerare described in the text.

1806

relationships of locust flight muscle (Neville, 1965; Nevilleand Weis-Fogh, 1963).

Both the force and distance transducers, as well as thepreparation, were mounted on short 6 mm diameter brassor light alloy rods clamped in specially machinedholders bolted to the Prior micromanipulators. Allmicromanipulators were mounted as close as possible to a12 mm thick machined-steel baseplate using magneticstands. Tests in which a force of 1 N was applied across theapparatus showed that the movement between the endsupports was less than 10 µm.

Stepwise force calibrations using weights and stepwisedistance calibrations were carried out during every experiment,and also provided a test of the linearity of the response of theapparatus.

Data collection and analysis

One force transducer was connected to a MacLab bridgeamplifier with a bandwidth of 2 kHz.

Most force and distance data were recorded on separatechannels of an Analog Digital Instruments MacLab 4 12-bitdata-acquisition system using Chart 3.5 software at up to1000 samples s−1 with the channels sampled alternately, notsimultaneously. Some force–distance measurements were alsomade using Scope 3.5 software at sampling rates of 4 or10 kilosamples s−1.

The software allowed baselines and scales to be defined.Using the x–y display, force versus distance work loops werecalculated directly. The work done or released was thenobtained as the area under different regions of the work loops.

Measurements of the force–distance relationships of tymbalbuckling

The insect preparation was mounted on onemicromanipulator with its long axis parallel to the baseplate.The stiff force transducer (Fig. 2) was mounted on anothermicromanipulator with its probe rod also parallel to thebaseplate. Using one protractor placed on the rod on which theinsect was mounted and another on the baseplate, the positionof the insect could be adjusted so that the angle of push on thetymbal plate could be varied from 110 ° to a practicalmaximum of 170 ° above the mid-ventral line of the insect andfrom 90 to 120 ° relative to the anterior-to-posterior long axisposition (0 ° by 0 ° was taken as mid-ventral and anterior: seeFigs 3A,B, 11). The precision of these settings was less than±3 °.

After the force and distance transducers had been zeroed, theinsect was brought towards the probe rod of the forcetransducer until contact was detected as a positive forcetransducer reading. The vertical and horizontal positions of theinsect were adjusted so that the tip of the probe rod entered theapodeme pit on the tymbal plate (Figs 1, 3C). Force anddistance recordings were then made as the probe rod wasmoved forwards and backwards rapidly over a distance of0.5–0.8 mm; with practice, the complete in–out movement wasachieved in 0.3–0.4 s. Force versus distance loops were then

plotted using the MacChart or MacScope software; these loopswere highly consistent (see Fig. 6).

At the end of each series of measurements, the angle of theprobe rod was changed by 10 ° relative to the coordinates ofthe insect body, and another series of measurements was made.In most cases, 10 measurements were made at 200 samples s−1

followed by a further 10 at 1 kilosample s−1. Somemeasurements were also made using MacScope to providegreater temporal resolution.

Measurements of muscle contractions

Tymbal muscle preparations were used in situ and as far aspossible in their normal orientation. Using a live animalprepared for brain stimulation, a stainless-steel wire stirrup wasattached with cyanoacrylate glue to the outside of the tymbalplate, with the centre of the stirrup set to pull along the line ofthe tymbal apodeme. After the glue had set, a ring of cuticlewas cut away round the stirrup, detaching the apodeme andstirrup from the tymbal. The stirrup was then connected to aforce transducer via a 20 mm long loop of 0.3 mm diameterstainless-steel wire.

Force and distance measurements were made using the morecompliant force transducer. Muscle contraction was elicited bybrain stimulation (as described above): typically, a brief stimulusresulted in a train of between 5 and 20 muscle contractions.

The temperature of the preparation was measured using a0.2 mm diameter thermocouple placed inside the abdominal airsac of the cicada. The thermocouple was connected to a BaileyBAT 12 thermometer. The insect’s internal body temperaturewas raised from the ambient temperature of 24–25 °C to amaximum of 39 °C using a 60 W bench lamp. Repeatexperiments at 28 °C before and after heating to 39 °Cproduced closely similar force and distance recordings.

Measurements of the sound field around the singing insect

Sound pressure levels were measured using a Bruel andKjaer 2230 sound level meter and Bruel and Kjaer 4155microphone. The sound level meter was set to measure theimpulse peak maximum of the sound (which, for a continuouspure-tone signal, is 3 dB higher than the root mean square valuethat is normally quoted as the sound pressure level).

Checks on the validity of the readings obtained were carriedout as follows. The 1 kHz waveform produced by a Bruel andKjaer type 4230 calibrator, giving 94 dB root mean squaresound pressure, was recorded via the alternating current outputsocket of the sound level meter using MacScope. The peakvoltage of this recording was then compared with the peakvoltage of recordings of the insect sounds produced by brainstimulation. This procedure gave values that were within0.2 dB of those shown by the sound level meter.

The microphone was positioned 100±1 mm from the ventralsurface of the insect at the opening of the tympanal opercula.The insect was rotated in a series of 45 ° steps, first around thetransverse plane, then in planes 45 ° anterior and 45 ° posteriorto the transverse plane, and finally readings were taken 100 mmstraight in front of and behind the insect on the long axis. After



a set of readings around the insect had been completed, afurther set of readings was taken with the microphone in thestarting position to check that the insect was still producing thesame sound level.

The preparation was placed above an 85 mm thick sheet ofSonex anechoic foam. Further sheets of foam were insertedbetween the preparation and the support stands, and around thesides and over the top of the preparation. There was no evidenceof echoes in our recordings of song made in these conditions.

Five sound pressure measurements at 0.1 m range weretaken at each position. The highest of these measurements wasconverted to the equivalent range (in m) for a peak sound

pressure level of 90 dB (equivalent to a sound intensity of10−3 W m−2) using the following equation:

range = 10[(dB measurement − 90)/20] × 0.1 . (1)

These ranges were then used to draw 90 dB isobars of thesound field.

Calculations of the ratio of peak to mean power in the songwere made from field recordings of singing cicadas made in1988 by D. Young, using a Nagra IVS tape recorder andSennheiser MKH816 microphone. Portions of songcontaining two or complete three sound pulses were recordedonto MacScope at 100 kilosamples s−1. Pulse period was

Tymbalapodeme

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Operculum

Dorsal

Ventral

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Tymbalmuscle

Tymbalmuscle

Tymbalmuscle

Tymbalwith ribs

Abdominalair sac

Abdominal air sac

OperculumTympanum

Chitinous V

Base ofchitinous V

Flight muscles

Head

A B C D

A

BC

D E

Fig. 3. (A–C) Drawings of theanatomy of Cyclochila australasiae toshow the tymbal and tymbal muscles.(A) Side view, with the anterior part ofthe abdomen cut away to the mid line,to show the shape of the tymbalmuscle, its origin and its insertion; thedashed lines show the angles of themuscle fibres relative to the horizontalplane (labelled 0 ° and 180 °).(B) Posterior view of the firstabdominal segment to show the shapeof the tymbal muscles, their origins onthe chitinous V and their insertions onthe tymbal apodemes. The dashed linesshow the angles of the muscle fibresrelative to the sagittal plane (labelled0 ° and 180 °). (C) Dorsal view of theposterior end of the thorax and anteriorend of the abdomen, with the dorsalcuticle cut away to show the tymbalsand tymbal muscles. Part of the dorsalcuticle and tymbal have been cut awayon the right side to show the tymbalapodeme and the dorsal end of thetymbal muscle. B and C are drawn tothe same scale. (D,E) Diagramscorresponding to B and C to show theangles at which the strap-like region ofthe tymbal apodeme meets theapodeme pit on the tymbal plate(shown as circles). In D, the tymbalplate is shown as a vertical section andin E as a horizontal section, bothdrawn through the apodeme pit.

1808

measured from the MacScope recordings and used to obtainpulse frequency. Pulse duration was taken as the time fromthe start of the pulse to its decay to 10 dB below the peaklevel (Fig. 4A). The mean sound intensity of the pulses wascalculated from the same recordings, following the proceduredescribed below and illustrated in Fig. 4B. (This method ofcalculating mean sound intensity is similar to that used inBennet-Clark, 1970.) (1) The sound level meter reading (indB at 100 mm range) gave the amplitude of the loudest cyclein the song pulse as a sound pressure (as given by the peakimpulse reading). (2) A digitised oscillogram of two pulsesof song was made (see Fig. 4A). (3) The data from stage 2were squared (see Fig. 4B). (4) The mean of the data setobtained in stage 3 was calculated (this gives a relativemeasure of the mean sound power in the pulse). (5) The ratioof the mean value of the sound power to the square of theamplitude of the largest cycle in the pulse was calculated (theamplitude of the largest cycle is obtained from stage 3).Stages 2–5 were all calculated by the MacScope software. (6)The fractional peak power to mean power ratio was convertedinto a ratio in dB (a power ratio of 10:1=10 dB). (7) The meansound intensity, integrated thoughout the pulse (in dB) wasobtained by subtraction of the values obtained in stages 1 and6. 90 dB is a sound intensity of 1 mW m−2 equivalent, in aplane wave, to a sound pressure of 0.63 N m−2. (8) The meansound intensity at 100 mm was converted to the range to a90 dB isobar using equation 1. (9) The mean sound power inthe song (in mW) is given by the area of the 90 dB isobar (inm2).

The total surface area of the sound field of the three-dimensional map that was built up was then used to calculatethe peak sound power output of the insects. This was convertedto an estimate of the mean power output using the peak powerto mean power ratio obtained for field records of calling song(see Table 2).

Although our sound level measurements were recorded tothe nearest 0.1 dB or ±2.4 %, the realisable precision of thesemeasurements is unlikely to be better than ±0.5 dB or ±12 %because of inaccuracies in other parts of the measuring chain.

Terminology and conventions

Sound pressure levels are quoted throughout this studyin decibels (dB) relative to the accepted threshold: 0 dB=20×10−6 N m−2 (or relative to 20µPa). This sound pressure levelis equivalent, in the plane wave conditions that prevail here, toa sound intensity (power per unit area) of 10−12 W m−2.

Relative power is measured on a logarithmic scale indecibels. 10 dB is a 10-fold power ratio (=101). A 1 dBratio=100.1 or a power ratio of 1.26. Sound power isproportional to the square of sound pressure level. Therefore,a 10 dB power (or sound intensity) ratio is equivalent to asound pressure ratio of √10 or 3.16. Whether the power ratiois multiplicative or divisive is indicated by the sign: −3dB or‘3 dB below’ indicates a power ratio of 10−0.3 (1:0.5) or halfpower. For a fuller discussion of these relationships, see Olson(1957) or Fletcher (1992).

ResultsThe anatomy of the tymbal and its muscle

The anatomy of the tymbal of C. australasiae has beendescribed previously in some detail (Young and Bennet-Clark,1995; Bennet-Clark, 1997) (Fig. 1). The tymbal muscle insertson the apodeme, which is connected to the tymbal plate via ashort flexible strap-like length of the apodeme (Fig. 3C). Thedorsal region on the tymbal plate from which the tymbal apodemeinvaginates forms a discrete pit approximately 0.15mm indiameter. This apodeme pit acts as the focus for the forceproduced by the tymbal muscle and also forms a convenient sitefor external application of force via a probe rod (Fig. 1).

The tymbal muscle consists of a bundle of long fibres whichextend from the sternal origin to their insertion on the tymbalapodeme. At the ventral origin on the chitinous V of the firstabdominal sternite (Fig. 3B,C), the cross section of the muscleis approximately oblong, but the cross section becomesapproximately circular at the tymbal apodeme (Fig. 3C). Themuscle has the following measurements (mean ± S.D.): musclemass 87.1±14.3 mg (N=10); muscle fibre length 7.59±0.37 mm(N=8); and apodeme insertion area 13.0±1.77 mm2 (N=7).

Viewed from normal to the sagittal plane (Fig. 3A), thefibres form a truncated triangle which is broader at the ventralorigin of the muscle on the chitinous V. The most anteriorfibres run upwards and backwards at 110 ° to the animal’s mid-ventral line, and the most posterior run upwards and forwardsat 60–65 ° to the mid-ventral line, with the centre of the muscle


-2

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ativ

e so

und

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sure

leve

l (V

)R

elat

ive

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er (

V2 )

Peak power 1.60 V2

Mean power 0.202 V2

A

B

Peak power to mean power ratio = 7.92:1 (9.0 dB)

Pulseduration

Pulse period

Fig. 4. The calling song of Cyclochila australasiae. (A) Oscillogram oftwo pulses of song, recorded in the field, showing the terminology usedto define the components of the song: pulse duration is taken as the timefrom the start of the pulse to its decay to 10dB below the peak level.The oscillogram shows relative sound pressure, as the output voltage ofthe tape recorder, versus time. (B) Oscillogram of the relative power inthe two song pulses shown in A. The voltages shown in A have beensquared, and the ratio between the peak and mean values of (voltage)2

has been calculated for the two song pulses illustrated in A, both as aratio and as a relative ratio in dB. These calculations followed theprocedure explained in steps 2–6 of the section of Materials andmethods entitled Measurements of the sound field around the singinginsect. The recordings were made at 100kilosampless−1.


block running at approximately 85 °. Viewed from behind (Fig.3B), the fibres of the tymbal muscles run from close to themidline at their ventral origins to their dorso-lateral insertionson the tymbal apodemes at angles between approximately152 ° and 165 ° to the mid-ventral line, with the centre of themuscle block running at approximately 160 ° to the mid-ventralline.

Viewed from the posterior, the dorsal regions of the tymbalplates lie at an angle of approximately 20 ° either side of thesagittal plane. The strap-like distal part of the apodeme of thetymbal muscle, which is aligned with the central axis of thetymbal muscle, meets the tymbal plate at approximately 155 °to the sagittal plane and thus at approximately 45 ° to the dorso-ventral axis of the tymbal plate (Fig. 3D). Viewed from above,the tymbal plates lie at angles of approximately 45 ° either sideof the insect’s long axis, and the strap-like regions of theapodemes run at 95 ° to the long axis, meeting the tymbal platesat approximately 50 ° to the horizontal axis of the plate(Fig. 3E). Taking the angles of 45 ° to the dorso-ventral axisand 50 ° to the horizontal axis of the tymbal plate, we calculate,by simple trigonometry, that the apodeme runs at an angle ofapproximately 36 ° to the plane of the tymbal plate.

The effect of altering the position and direction of the appliedforce

The force required to push the tymbal plate inwards risessteadily until, suddenly, the tymbal ribs buckle inwards,releasing energy. The force–distance relationships of the

inward movement were affected both by the position of theprobe rod on the tymbal plate relative to the apodeme pit andby the angle or direction of the push of the probe rod.

Because the tymbal muscle pulls in a linear manner via itsapodeme on the apodeme pit on the tymbal plate (Fig. 1) alongthe main trajectory of the muscle (Fig. 3), we tested the effectof changing both the position on the tymbal plate and the angleat the apodeme pit at which force was applied by the probe rod.

The effect of moving the probe rod vertically on the tymbalplate from 0.4 mm dorsal to the pit (the dorsal edge of thetymbal plate) via the apodeme pit to 2 mm ventral to theapodeme pit is shown in Fig. 5A for a push approximatelynormal to the surface of the tymbal plate, at 120 ° behind theinsect’s anterior in the horizontal plane and 140 ° above themid-ventral line in the sagittal plane. Both the force requiredand the distance through which the probe rod had to be movedto bring about tymbal buckling were maximal when the tip ofthe probe rod was positioned in the apodeme pit.

The work required to bring about inward buckling of thetymbal, assuming that the tymbal obeys Hooke’s law (seeFigs 6, 7), is given by 0.5 (force at buckling × distance atbuckling). Fig. 5A shows that the work required was maximalwhen the tymbal plate was pushed inwards at the apodeme pit,but that only one-tenth as much work was required when thetymbal plate was pushed inwards 2 mm ventral to the apodemepit.

The effect of altering the angle of push on the apodeme pitis shown in Fig. 5B. It was difficult to make measurements at

Table 1. Force versus distance relationships and energy storage – release relationships for tymbals of Cyclochila australasiae

Variable Mean±S.D. Range

Maximum force at buckling (N) 0.38±0.08 0.28–0.55Distance to buckling (µm) 368±84 300–620Force decrease when rib 1 has buckled (N) 0.09±0.03 0.06–0.13Residual force after all ribs have buckled (N) 0.17±0.04 0.10–0.25Total energy in work loop (µJ) 75.5±27.5 43.5 to 119Energy released by buckling of rib 1 (µJ) 16.5±7.5 8.8–28.2Energy released by buckling of all ribs (µJ) 45.1±18.6 20.1–74.2Energy available for outward movement (µJ) 32.8±12.2 18.3–56.7

N=11, except for the force decrease and energy release from the buckling of rib 1 where N=6.

Table 2. Characteristics of the calling song of Cyclochila australasiae

Variable Mean ± S.D. Range

Pulse frequency (Hz)* 234±10.9 220–255Pulse period (ms) 4.27±0.19 3.92–4.54Pulse duration (ms) 2.47±0.46 1.43–3.09

(see Fig. 4A) Duty factor, pulse duration:pulse period 0.57±0.11 0.32–0.74Peak power to mean power ratio 8.51±1.70:1 5.12–12.6Peak power relative to mean power (dB) +9.30±0.90 7.09–11.0

Values are means ± S.D. for N=7 insects. For each insect, five sections of the calling song recordings, each consisting of two complete pulses,were measured.

For each variable, the mean ± S.D. was calculated from all 35 song samples, and the range of the values is also given.*The two tymbal muscles contract alternately and in antiphase so that the rate of contraction of each is half the pulse frequency.

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angles of push of over 170 ° to the mid-ventral line or at anglesof push anterior to the insect’s transverse plane because theprobe rod tended to slip out of the apodeme pit. At angles ofpush of more than approximately 130 ° behind the insect’santerior, the probe rod tended to be obstructed by the cuticleof the tymbal frame (see Fig. 3C). It also proved difficult toobtain consistent results, probably because of the difficulty ofpositioning the tip of the probe rod in the same place on the

tymbal plate after changing the angle of the probe rod.However, the same general trend was observed with 10tymbals: the force required to cause buckling and the distancethrough which the probe rod had to be moved before bucklingoccurred both approximately doubled as the angle of push wasincreased from 110 ° to 170 ° above the mid-ventral line. Thisis shown for one tymbal in Fig. 5B. The effect of altering thedirection of push relative to the insect’s anterior–posterior axiswas less marked (results not shown).

Energy storage and release by the tymbal

The force required to move the tymbal plate inwardsincreased steadily as the tymbal plate was pushed, until thetymbal ribs buckled (Figs 6, 7), when the force fell rapidly toless than half its peak value. Further inward movement wasaccompanied by a further increase in the force. As the proberod was withdrawn, the force decreased more or less steadily,increased slightly as the tymbal ribs clicked outwards, thendecreased again until the probe rod was removed from thetymbal plate. For any one preparation, the work(force–distance) loops that were obtained were highlyrepeatable (Fig. 6).

In summary, the work loops contain the following stagesafter contact between the probe rod and the apodeme pit: theseare numbered on Fig. 6. (1) Energy is stored elastically duringthe initial phase of the inward movement; during this phase,the force rises approximately linearly. (2) The force decreasesin a stepwise fashion as successive tymbal ribs buckle inwards.(3) After all the ribs have buckled, further inward movementof the tymbal plate causes further elastic distortion of thetymbal. (4) The initial part of the outward movement of thetymbal shows an elastic, but non-linear, release of theremaining stored energy. (5) During the latter part of theoutward movement, the force increases as the tymbal ribsbuckle outwards. (6) Finally, the force decreases to zero as theprobe rod is removed from the tymbal plate.

The course of the storage and release of energy is shown in


φ

Position of pushon tymbal plate (mm)

Wor

k re

quir

ed to

buc

kle

tym

bal (

µJ)

Forc

e re

quir

ed to

buc

kle

tym

bal (

N)

0

20

40

60

80

100

Dis

tanc

e m

oved

bef

ore

buck

ling

(µm

)10123

0

0.1

0.2

0.3

0.4

0

100

200

300

400

500

Ventral

At pit

Forc

e re

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ed to

buc

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tym

bal (

N)

Dis

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oved

bef

ore

buck

ling

(µm

)

180150120900

0.2

0.4

0.6

0

200

400

600

Force

Distance

Angle of push above mid-ventral, φ (degrees)

A

B

Force

Distance

Work

Tymbalplate

Apodemepit

Do

Ve

Ribs

0°

Dorsal

Fig. 5. Effects of altering the position and angle of push on the forceversus distance relationships of tymbal buckling in Cyclochilaaustralasiae. (A) Graph showing the force, distance and workrequired to cause tymbal buckling when pushed at the apodeme pit orat positions dorsal and ventral to the pit. In this preparation, thedirection of the push was 120 ° behind the insect’s anterior and 140 °above its mid-ventral line. The inset shows the positions of the pointsat which the tymbal was pushed (filled circles), cited dorsally (Do)and ventrally (Ve) relative to the apodeme pit on the tymbal plate.(B) The force and distance required to cause tymbal buckling whenpushed at the apodeme pit at angles between 110 ° and 170 ° abovethe insect’s mid-ventral line at an angle in the horizontal plane thatwas 110 ° behind the insect’s anterior. The dotted line at 155 ° showsthe approximate angle of pull of the tymbal muscle apodeme. Theinset shows the angle of push relative to the insect’s mid-ventral line;the conventions adopted here are also used in Figs 3 and 11.

-200 0 200 400 600

0

0.1

0.2

0.3

0.4

0.5

Forc

e (N

)

Distance strained (µm) 800

Rib 1 in

Rib 2 in

Ribs out

Inwards

Outwards

2 3

45

6

1

Fig. 6. Force versus distance work loops for one tymbal ofCyclochila australasiae. In this plot, ten successive loops aresuperimposed to show the repeatability of the measurements. Thearrows show the direction of the work loops. The numbered stages ofthe in–out movement described in the text are shown here bynumbers 1–6. Recorded at 1000 samples s−1.


detail in Fig. 7 for one tymbal which was pushed at 150 ° abovethe mid-ventral line and at 110 ° to the anterior. The timecourse of the changes in force together with the distance movedinwards then outwards is shown in Fig. 7A, and theforce–distance work loop is shown in Fig. 7B. The initial phaseof energy storage for this particular tymbal was almost linear.Slightly concave and convex force–distance curves wererecorded from other tymbals. Peak forces before tymbalbuckling of between 0.28 and 0.55 N were recorded from 11tymbals (Table 1).

This initial phase of movement of the tymbal plate wasessentially elastic. Experiments in which the tymbal waspushed inwards and released over distances that allowed thetymbal plate to return outwards before buckling had occurredshowed a force versus distance pattern that closely mirroredthat during the inward phase (Fig. 8). This suggests that, duringthe first part of the inward movement that precedes ribbuckling, the elastic surround (Fig. 1) acts as a simple springcontrolling the movement of the tymbal plate.

Previous work has shown that tymbal buckling occurs in aseries of steps as successive ribs buckle inwards (Simmons andYoung, 1978; Young and Bennet-Clark, 1995; Bennet-Clark,1997). Typically, the inward buckling of the first two or threeribs occurred over a time span of 1–3 ms, each of whichproduced a pulse of sound.

Buckling of the tymbal ribs was always accompanied by adecrease in force and thus a release of energy by the elasticregions of the tymbal. In most cases, it was difficult to measurethe precise contribution of the buckling of each individual rib

In

0 200 400

0

0.1

0.2

0.3

0.4

Forc

e (N

)

Distance strained (µm)

Rib 1 in

Rib 2 in

Rib 3 in

Ribs out

Energystorage

Energyrelease

0

0.1

0.2

0.3

0.4

Forc

e (N

)

0 200 400Distance strained (µm)

26 µJ

14.8 µJ

23 µJ

5.6 µJ

B

C

Total energyin cycle,69 µJ

Ene

rgy

rele

ased

46

µJ

40200

0

Time (ms)

0.2

0.4

Forc

e (N

)

-200

0

200

400

Dis

tanc

e (µ

m)Force

Distance

AOut

Elastic recovery

Fig. 7. Force relationships and work loop of a tymbal. (A) The forceapplied (thin line) and distance moved (thick line) during a rapid in-then-out movement of the probe rod. The force initially rises almostlinearly throughout the inward movement until the tymbal ribsbuckle rapidly, then remains almost constant over most of thesubsequent outward movement. Recorded at 1000 samples s−1. (B) The force–distance work loop from A. The inset shows thedirection of the loop and the processes that occurred. (C) The workloop in B is shown broken into its energy components. The energyreleased by successive rib buckling is shown as separate cross-hatched regions, and the residual energy that is available for elasticrecovery of the tymbal and its muscle is shown stippled.

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600Distance (µm)

Rib 1 in

Rib 2 in

Rib 3 in

Inward strain

Partial relaxation and re-strain

0

0.2

0.4

0 100 200 300 400 500 600Time (ms)

Forc

e (N

)

In

Out In

Rib buckling

Forc

e (N

)A

B

Compliance 800 µm N-1

Fig. 8. (A) Force versus time curve showing an in–out movementthat did not cause the tymbal ribs to buckle (0–300 ms) followed byan inward movement that caused the ribs to buckle (from 450 msonwards). The arrows show the direction of movement of the proberod. (B) Graph of force versus distance for the movement shown inA, indicating that the partial elastic recoil and subsequent re-strainthat occurred between 120 ms and 520 ms in A is essentially elastic.Note, too, that in this preparation, the buckling of successive tymbalribs can be seen. The arrows show the directions of the componentsof the trace. The dashed line has a slope equivalent to a complianceof 800 µm N−1. This trace was recorded at 4000 samples s−1 and,because of limited recording time at this rate, only shows the inward-going part of the tymbal movement.

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to the course of the release of energy, but Fig. 7B shows a workloop in which the stages of buckling can be distinguished. Inthis example, the force fell to approximately two-thirds of themaximum value as rib 1 buckled and then to approximatelyhalf the maximum as rib 2 buckled.

The force–distance relationships of the outward recoverymovement after buckling tended to be markedly non-linear(Figs 6, 7). In many cases, the force remained almost constantfor most of the movement but showed a small increase, nearthe end of the movement, as the tymbal ribs buckled outwards.

The areas of the force–distance loops give the energy storedand dissipated in different stages of the inward and outwardmovement. These areas and the associated storage and releaseof energy are shown for a typical force–distance loop inFig. 7C. Initially, the force rises until the first tymbal ribbecomes unstable and buckles inwards suddenly, with anaccompanying rapid decrease in force and release of storedenergy, followed in sequence by buckling of the other tymbalribs. Of the total 69 µJ energy stored during the initial inwardmovement, approximately two-thirds (46 µJ) was dissipated asthe tymbal buckled inwards, leaving the remaining one-third(23 µJ) available to re-extend the tymbal muscle and restore thetymbal to its resting position with the ribs buckled outwards.

Values for the force–distance relationships of 11 tymbals aregiven in Table 1. The force–distance relationships and thework loops of the tymbal shown in Fig. 7 are taken from atymbal with properties close to the mean values reported inTable 1. Note that the measurements of distance assumed thatthe body of the cicada did not move when force was appliedto the tymbal plate. In reality, it is likely that a small, but hard-to-measure, part of the inward movements that we recordedoccurred as a result of distortion of the cicada abdomen.Consequently, the distances and energy values reported inTable 1 are likely to be slight overestimates.

Energetics of the tymbal muscle

The experiments reported below were carried out at the endof the season when fewer animals were available. The force,distance and work output of the tymbal muscle were measuredto determine whether these variables were compatible with themechanical properties of the tymbal. Preliminary results arepresented here, although incomplete, because of theirrelevance to our other findings.

The activity of the tymbal muscles was recorded in responseto contractions elicited by brain stimulation. In all cases, themuscle contraction rate was lower than the rate of 117 Hz foreach muscle that occurs in calling song, but in threepreparations we recorded rates of 75–80 Hz at 28 °C. Force anddistance were recorded simultaneously: Fig. 9 shows anexample of the force–length curves that were obtained with themuscle driving the compliant force transducer. The mean valueof the peak active force recorded from seven preparations was0.31±0.04 N (mean ± S.D.) and the mean change in length orstrain of the work loop was 295±41 µm. This force iscomparable with the value of 0.295 N obtained by Josephsonand Young (1981) using C. australasiae (using an area of13 mm2 for the tymbal muscle apodeme) and the values forforce per unit area cited by Josephson and Young (1981). Themean distance of shortening obtained here is 3.9 % of themuscle fibre length. The total work produced by thecontraction of the muscle is given by the area of theapproximately triangular region below the ends of thelength–distance plot (Fig. 9). The mean work was47.0±11.2 µJ (N=7) (mean ± S.D., range 30–61.3 µJ).

Note that the measurements of distance have assumed thatthe body of the cicada does not move when force is producedby the tymbal muscle. However, it is likely that a small, hard-to-measure, part of the inward pull by the tymbal musclebrought about an inward distortion of the cicada abdomen.


56 µJ

0100200300400

0

0.1

0.2

0.3

0.4

Distance shortened (µm)

Forc

e (N

)

Fig. 9. Force versus distance shortened for a burst of contractionsproduced by a tymbal muscle at 29 °C after activation by brainstimulation. The x axis shows the distance shortened relative to theunstimulated length of the muscle. Five loops were measured at10 000 samples s−1. The stippled area shows the work done by themuscle on the springs of the force transducer, which had a similarcompliance to that of the tymbal.

50 W kg-1

100 W kg-1

150 W kg-1

200 W kg-1

Strain at which tymbal buckling occurs (µm)

Forc

e re

quir

ed to

buc

kle

tym

bal (

N)

Fig. 9work area

Range of forces and strainsrequired to buckle tymbal

60050040030020010000

0.2

0.4

0.6

0.8

Fig. 10. The mass-specific power output that would bring aboutbuckling of tymbals of different mechanical properties. Tymbalmuscle mass is taken as 87 mg, and the contraction frequency is117 Hz. The circle shows the power produced by the muscle shownin Fig. 9, assuming a contraction rate of 117 Hz. The filled squareshows the means ±1 S.D. (N=7) of the force and distance that causetymbal buckling (see Table 1).


Consequently, the distances shortened and the energy valuescalculated above are likely to be underestimates.

We measured the effect of pre-stressing the muscle in threepreparations. Passive stresses of 0.6 N could be appliedreversibly. With passive stresses between 0.05 and 0.3 N, wefound that the muscles produced force–distance plots that wereclosely similar in shape and area; in other words, over thisrange of passive stresses, the muscle appeared to produce asimilar active stress over a similar distance of activeshortening. With passive stresses less than 0.05 N or greaterthan 0.4 N, the active force became smaller. It thus appears thatthe muscle can contract over a range of passive stresses andlengths and still produce similar amounts of work per cycle ofcontraction.

In one preparation, raising the internal body temperaturefrom 27 to 39 °C caused the rate of activation and contractionof the muscle following brain stimulation to increase from 73to 97 Hz. Extrapolating from these data, the contraction rate of117 Hz observed during singing would require a muscletemperature of approximately 42 °C. This temperature iscomparable to the temperatures of 41–45 °C recorded for thetymbal muscles of the cicada Okanagana vanduzeei duringsinging (Josephson and Young, 1985).

The work areas we obtained from the tymbal muscles arebroadly compatible with the work required for buckling of thetymbal (c.f. Fig. 9 and Table 1). Taking a mean musclecontraction rate of 117 Hz during singing and a mean musclemass of 87 mg, we can calculate the specific muscle power thatis required to buckle the tymbal. Fig. 10 shows how the forcerequired for tymbal buckling and the inward strain of thetymbal equate with the mass-specific muscle power of thetymbal muscle. From Fig. 10, it appears that the tymbal musclemust produce between 75 and 125 W kg−1 to account for theobserved performance.

Mean-to-peak power ratio of the song

Using recordings of the calling song made in the field by D.Young, the structure of the songs of seven C. australasiae wasmeasured and analysed. Variables describing the temporal

structure of the song were calculated from oscillograms (seeFig. 4A for terminology) and are given in Table 2. The ratioof peak power to mean power in the song waveform wascalculated according to stages 2–6 of the procedure laid out inMaterials and methods and illustrated in Fig. 4B.

The sound field around the singing insect and the mean soundpower

Sound fields were measured around three insects in whichsound production was elicited by brain stimulation. The soundwas loudest mid-ventrally and quietest along the body axis inthe horizontal plane either directly anterior or directly posteriorto the insect but, overall, the sound radiation pattern onlyshowed a difference of 3 dB between the loudest and quietestdirections.

These measurements were converted to give the effectivesize of the 90 dB sound pressure isobar as if the insect wereproducing normal calling song. The values for the peakimpulse maximum sound pressure that had been made at100 mm range were converted first by subtraction of 9.2 dB togive the mean sound intensity at that range. This value thenwas used to calculate the range to 90 dB sound pressure isobars(Fig. 11).

For the example shown in Fig. 11, the 90 dB sound isobar(equivalent to an intensity of 1 mW m−2) is approximatelyequivalent to an ellipsoid of radii 0.50 m×0.50 m×0.55 m. Thesurface area of this ellipsoid is 3.45 m2. Thus, the mean soundpower output of this particular insect was 3.45 mW; estimatesfrom two other insects were 3.15 mW and 7.0 mW.

The peak sound pressures we measured are comparable withthe values reported by Young (1990) for the same species. Wefound peak sound pressures of 116.2, 116.8 and 118.9 dB at100 mm range for the three animals for which we had completerecordings. These are equivalent to 110.2–112.9 dB at 200 mmrange. At 200 mm range, Young reported mean values of109.9 dB +1.8 or −2.3 dB (mean ± S.D., N=5) for the protestsong and 112.9 dB +2.9 or −4.4 dB (N=8) for the calling songof C. australasiae. The equivalent mean sound powers are3.15 mW for the protest song and 5.1 mW for the calling song,

Range to 90 dBisobar inhorizontal plane

0°

90°

180°

270°

0°

90°270°

180°

Range to 90 dBisobar intransverse plane

0°

270°

225°

180°

90°

45°

0.8 m

135°

315°

0.4 m

BAFig. 11. (A) Polar plot of the sound distribution arounda Cyclochila australasiae in which singing wasinduced by brain stimulation. The plots show the radialdistance from the tympanal opercula of the 90 dBmean sound pressure level isobar, plotted at 45 °intervals around the body, in both the horizontal (opencircles, broken line) and transverse (filled squares,solid line) planes. The horizontal and transversepatterns are approximately circular: these are shown asstippled circles, respectively 0.5 m radius concentricwith the open circle at the centre of the plot and0.55 m radius centred at the central filled square.(B) Diagrams of the body of the insect showing theconventions used for the coordinates of the polar plots.Upper: in the horizontal plane, where 0 ° is taken asanterior. Lower: in the transverse plane, where 0 ° is taken as mid-ventral (these are the same coordinates as were used in Figs 3 and 5). Theboxes show the symbols and the stipple patterns used for the equivalent circles.

1814

assuming the same radiation pattern as in the present study,suggesting that the sound powers we measured in response tobrain stimulation may be approximately two-thirds of thoseobtained under natural conditions (or approximately 2 dBlower).

The energy in each song pulse is the mean sound powerdivided by the song pulse rate (14.7 µJ assuming a pulse rateof 234 Hz, range 13.5–30 µJ in the present study and 13.5 µJand 21.5 µJ for protest song and calling song from Young,1990). These values can be compared with the work releasedby the buckling of all tymbal ribs in each cycle of tymbalbuckling (Fig. 7; Table 1) for which a mean value of 45.1 µJwas obtained, which is substantially greater than thatcalculated for the song pulses.

DiscussionThe tymbal as a rapid-release energy-storage mechanism

Mechanisms in insects by which energy is stored slowly andreleased rapidly include the generation of sound pulses incicadas (Pringle, 1954) and moths (Blest et al., 1963) as wellas the catapult mechanism of jumping fleas (Bennet-Clark andLucey, 1967) and many other fast-acting systems (for a review,see Gronenberg, 1996).

Previous experiments have shown that the tymbals ofcicadas produce discrete clicks of sound as the ribs buckleinwards (Pringle, 1954; Simmons and Young, 1978; Bennet-Clark, 1997). The present work confirms these findings andprovides an energy budget for the elastic distortion of thetymbal and the release of energy that accompanies the bucklingof the tymbal ribs.

Previous work on the mechanical properties of the tymbalhas shown that the thick resilin pad at the dorsal end of thetymbal (see Fig. 1) is a major elastic determinant of theresonant properties of the tymbal (Bennet-Clark, 1997). Thetymbal apodeme attaches close to the dorsal end of the tymbalplate. The direction of pull along the apodeme is likely to causeboth an inward movement of the tymbal plate as a whole andalso an inward distortion of the dorsal resilin pad. The tymbalplate can be modelled crudely as if it were a rigid lever pivotedat its dorsal end in the resilin pad; its inward movement isopposed by the stiffness of the resilin pad and also by theresistance to buckling of the tymbal ribs.

If this tymbal plate lever is pushed inwards (or pulledinwards by its muscle), the applied force will have two maineffects: to distort the resilin pad and to produce a turningmoment about the effective pivot. The response of such asystem will be affected both by the position at which force isapplied and by the angle at which the force is applied. Theseare modelled in Fig. 12.

Consider two cases in which force is applied to differentregions of the tymbal plate: first at the apodeme pit where theforce is applied close to the pivot; and, second, ventral to theapodeme pit, close to the region in which the tymbal ribsbuckle (Fig. 12A). In the first case, a major effect will bedistortion of the resilin pad (Fig. 12A, upper right) and

comparatively little inward force will be applied to the tymbalribs, which will only buckle inwards after the application of alarge force on the tymbal plate. In the second case, there willbe a more direct effect on the tymbal ribs, which will buckleinwards with a smaller force (Fig. 12A, lower right). Weobserved a similar relationship between the force and distancerequired to cause buckling of the tymbal (Fig. 5A), whichsuggests that the tymbal is designed to maximise the amountof energy that can be stored prior to energy release by bucklingof the ribs.

Now consider the effects of altering the angle at which theforce is applied to the tymbal plate. Extreme cases are whenthe force is applied nearly parallel to the tymbal plate and whenthe force is applied nearly normal to the plate. In the first case,the turning moment will be small, but the distorting forceacting on the resilin pad will be large; in the second case, theturning moment will be larger, and the distorting force actingon the resilin pad will be smaller. These situations are modelledin Fig. 12B. The resultant force and distance required to causebuckling of the tymbal ribs were found to be smaller when thetymbal plate was pushed at angles close to the horizontal (ornearly normal to the plane of the tymbal plate) than when theangle of push was more nearly vertical and hence at an acuteangle to the plane of the tymbal plate (Fig. 5B). Here, also, itappears that the elastic regions at the dorsal end of the tymbalare designed to be distorted by the initial action of the tymbalmuscle and thus to store energy for release by the buckling ofthe tymbal ribs.

The tymbal ribs, however, are light-weight, thin structures(Young and Bennet-Clark, 1995; Bennet-Clark, 1997).Because buckling occurs approximately midway along theirlengths (Fig. 12A), buckling requires that a far greater force beapplied at the dorsal ends of the ribs than is required at thepoints of buckling; thus, the ribs act as a trigger mechanismthat is capable of retaining and then releasing large amounts ofstored energy.

The light weight and compliant nature of this triggermechanism ensure that the resonant properties of the tymbalwill be dominated by the stiffness of the elastic elements of thetymbal and by the mass of the tymbal plate (which exceeds thatof the heaviest rib by a factor of five; Bennet-Clark, 1997); thelightness and compliance also ensure that the force required toreset the trigger, by the buckling of the ribs back into theirconvex resting position, is far smaller than the force that mustbe applied to the tymbal apodeme to bring about inwardbuckling (Figs 6, 7), so the major part of the energy that isstored in the elastic elements of the tymbal is available fortransduction into sound.

The tymbal as a load and antagonist to a high-power muscle

To fulfil its role in sound production, the tymbal shouldprovide two types of loading to its muscle: it should store andthen dissipate the major part of the work done in each cycle ofmuscular contraction; it should also provide sufficient residualstrain energy to re-elongate the relaxing muscle. It seems likelythat the major elastic energy store is the resilin pad (Fig. 1),



which is a major determinant of the resonant frequency of thetymbal (Bennet-Clark, 1997), but the highly stressed tymbalapodeme may also store a proportion of the muscle energy. Thestrap-like region of the apodeme is relatively short and thin soits contribution to the energetics of the tymbal cycle isprobably minor.

The muscle contraction cycles described here suggest thatthe muscle is capable of producing an appropriate force overan appropriate distance to distort the tymbal to the stage atwhich it buckles inwards (c.f. Figs 7C and 9). The probablepower output from the muscle (Fig. 10) is approximately halfthe highest values reported for the sustained power outputfrom striated muscle (see, for example, Weis-Fogh andAlexander, 1977; Askew and Marsh, 1997), suggesting that

the loading provided by the tymbal may be very differentfrom the simple elastic load used here. In this context, itshould be noted that the singing insect adjusts the positionand dimensions of its abdominal resonator (Young, 1990),presumably to exploit its muscle power maximally; it is alsoable to alter the curvature of the tymbal, and presumably thework required to buckle it, by the activity of the tymbal tensormuscle (Pringle, 1954; Fonseca and Hennig, 1996), whichwill have similar effects.

The energetics of sound production

Sound production in a cicada such as C. australasiae occursas a series of links in a chain: a neural pattern initiates musclecontraction; the muscle contractions are converted into

70°

36°

0°

90°

Push at theapodeme pit

Push nearer theregion of rib buckling

Region at whichrib buckling occurs

Resilin pad Push stores energyby distortion of theresilin pad

Small force actingwhere the tymbalribs buckle

Little energy isstored in the resilinpad

Push acts close toregion at which ribbuckling occurs

Push at 36° to theplane of the tymbalplate

Push at 70° to theplane of the tymbalplate

Applied force anddistance vector

Resultant force anddistance vector normalto the tymbal plate

Tymbal plate

Long ribs

A

B

Fig. 12. Diagrams of the effects of pushing the tymbalplate at various positions and angles. In the left-handdiagrams, showing drawings of the tymbal, the directionof push is shown as lines in the plane of the plate, but theactual direction of push is assumed to be in a planeapproximately normal to the plate. The right-handdiagrams show how the push at different positions orfrom different directions acts on the tymbal. (A) Acomparison between the effect of pushing either at theapodeme pit or nearer to the region at which the tymbalribs buckle. The tymbal plate is modelled as a leversuspended by and pivoting at the dorsal resilin pad (seeFig. 1). When force is applied at the apodeme pit (rightupper), there is considerable distortion of the resilin padbut little force is applied at the region of rib buckling.When force is applied closer to the region of rib buckling(right lower), a relatively greater component of the forceis applied to the tymbal ribs but a smaller component isapplied to the resilin pad. The energy required forbuckling of the tymbal is greater when the push is at theapodeme pit than when the push is close to where the ribsbuckle (see Fig. 5A). (B) The effect of pushing at theapodeme pit at different angles to the plane of the tymbalplate (see Fig. 5B). When the angle of push runsobliquely to the tymbal plate (at 36 °), the component ofthe force vector acting normal to the tymbal plate will berelatively smaller than when the push runs more nearlynormal to the tymbal plate (at 70 °). The force required tobuckle the tymbal and the distance moved beforebuckling will be greater with a 36 ° push than with a 70 °push (see Fig. 5B). In the intact animal, the apodeme runsat an angle of approximately 36 ° to the plane of thetymbal (see Results and Fig. 3).

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mechanical work; the mechanical work is transduced intosound.

From the measurements reported in the present study, we canderive approximate values for the energy involved in the lasttwo links of this chain. A typical muscle contraction through0.30 mm produces a peak force of 0.32 N and thereby produces47 µJ of energy: these values are broadly compatible with,although somewhat lower than, the mean values required tobring about tymbal buckling (Table 2). As the tymbal buckles,it produces a train of pulses of increased air pressure within theabdominal air sac of the cicada, which excites and sustains asympathetic resonance in the abdominal Helmholtz resonator(Bennet-Clark and Young, 1992; Young and Bennet-Clark,1995), from which sound is radiated via the large ventraltympana (Young, 1990) (see Fig. 3B,C). Each pulse of the songis produced by a single muscle contraction and consequentinward buckling of one of the two tymbals. The mean energyin a pulse of the calling song is 21.8 µJ and the mean energyreleased by the buckling of all tymbal ribs is 45.1 µJ, but boththese values show variations of approximately ±35 %.

Taking the mean values for the energy of tymbal buckling(47 µJ) and the energy per pulse of calling song (21.8 µJ), theefficiency of transduction from mechanical energy to soundenergy appears to be approximately 46 %. Even using themaximum value for the energy that can be released by tymbalbuckling (74.2 µJ) and the lowest values for the energy persound pulse (13.5 µJ) gives a transduction efficiency of 18 %.

The very high efficiency that we ascribe to the mechanical-to-sound transduction process is similar to that suggested for asimilar process of transduction in the mole cricket Gryllotalpavineae (Bennet-Clark, 1970). This efficiency is far higher thanthe overall efficiency of the whole animal reported for thesound production of Gryllotalpa australis and the cricketTeleogryllus commodus (Kavanagh, 1987), which was foundto be 1.05 % and 0.05 % respectively. This reflects the fact thatwe are only examining the energetics of one or two links in thechain, rather than the energetics of the whole animal, asmeasured by Kavanagh (1987), which includes the energeticsof its physiological support systems.

Nonetheless, such a high apparent transduction efficiencydeserves further comment. Although the tymbal provides thepressure drive to the abdominal resonator (Young and Bennet-Clark, 1995), the sound is radiated through the large tympana,which are extremely thin (Young, 1990) and extend across thefull width of the abdomen. As such, the tympana provide asound source that can be modelled as a piston in an infinitebaffle. The coupling of a sound source to the fluid medium intowhich it is radiating depends on the specific acoustic resistanceof the source relative to that of the fluid medium (see, forexample, Olson, 1957; Fletcher, 1992). Calculations based onthe dimensions of the tympana suggest that their specificacoustic resistance is close to that of the air into which theyare radiating sound (Bennet-Clark, 1995). Thus, the extremespecialisation of the abdomen in male cicadas can be seen toresult in efficient mechanical to sound energy transduction and,for their size, the production of extremely loud sounds.

The experimental work reported here was largely carriedout at the University of Melbourne. This work was supportedin part by an Australian Research Council grant to Dr DavidYoung. We thank David Young for his support andencouragement throughout this work, for the loan of spaceand equipment and for allowing us to analyse his songrecords. This work was made possible by an Overseas StudyVisit Grant from the Royal Society to H.C.B.-C. andpermission to take sabbatical leave from Oxford Universityand St Catherine’s College, Oxford; this generosity isgratefully acknowledged. Special thanks are due once more tothe Department of Zoology, University of Melbourne, and toProfessor M. B. Renfree for hospitality throughout H.C.B-C’sstay in Australia, without which this work could not havebeen undertaken. We also thank two anonymous referees forconstructive comments on an early version of this paper.

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Energetics of cicada sound production

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