The Journal of Experimental Biology 202, 1803Ð1817 (1999) 1803 Printed in Great Britain © The Company of Biologists Limited 1999 JEB1998

TRANSDUCTION OF MECHANICAL ENERGY INTO SOUND ENERGY IN THE 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 , Parkville, 3052, *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

Summary The anatomy of the paired tymbal muscles of Cyclochila tymbal muscle produced mean values for the peak active australasiae was described. ForceÐdistance relationships of force of 0.31 N over 295 µm, which gave mean values for the sound-producing inÐout cycle of tymbal movement were the area of the work loops of 47.0 µJ. measured. The largest forces were measured when the push The calling song of C. australasiae had a mean pulse rate occurred at the apodeme pit on the tymbal plate at angles of 234 Hz (117 Hz for each side of the ). The peak similar to the angles of internal pull of the tymbal muscle. power to mean power ratio for the songs was 8.51:1 Initially, inward movement was opposed by the elasticity (+9.30 dB). Measurements of the sound field around of the tymbal, which stored energy. At a mean force of tethered and of the peak power to mean power ratio 0.38 N after a mean inward strain of 368 µm, the tymbal of the songs gave values for the mean power of the song of ribs buckled, the mean energy release being 45.1 µJ. The 3.15Ð7 mW; these correspond to an energy per song pulse energy release occurred over 2Ð10 ms in three or four of 13.5Ð30 µJ. Previously reported mean values are sound-producing steps as successive tymbal ribs buckled 3.15 mW for protest song and 5.1 mW for calling song. The inwards. After the ribs had buckled, the force decreased to efficiency of transduction of mechanical energy into sound a mean value of 0.17 N. The force returned to zero during energy is between 18 and 46 %. the outward movement, during which the tymbal ribs buckled outwards. The mean energy dissipated in the Key words: cicada, , tymbal, energy storage, outward movement was 32.8 µJ. During contraction, the transduction, sound radiation.

Introduction Cicadas produce sound by rapid buckling of a pair of domed rib adjacent to it buckles suddenly, becoming concave. This tymbals situated on the sides of the first abdominal segment rapid buckling movement and the resonant vibration of the (Pringle, 1954). Each tymbal is a highly specialised structure tymbal plate produce a pulse of sound. Further contraction of bearing an oval posterior sclerotised tymbal plate, anterior to the tymbal muscles causes the more anterior ribs to buckle; as which runs a row of narrow vertical ribs of sclerotised cuticle each subsequent rib buckles, a pulse of sound is produced (Fig. 1). These sclerites are separated by and surrounded by (Simmons and Young, 1978; Young and Bennet-Clark, 1995; strips of the elastic protein (Weis-Fogh, 1960; Scott, Bennet-Clark, 1997). In the Australian cicada Cyclochila 1970; Young and Bennet-Clark, 1995). australasiae, the tymbal plate plus ribs, in their elastic During sound production, the posterior tymbal plate is pulled surrounds, act respectively as the mass and compliant elements inwards by a large fast muscle (Pringle, 1954; Simmons and of a mechanical resonator (Bennet-Clark, 1997). Young, 1978). This tymbal muscle acts as the source of energy The vibration frequencies of this resonant system in C. in cicada sound production. Each muscle contraction appears to australasiae are close to the dominant frequency of the insect’s provide a train of store-then-release cycles of energy to the sound- song, so the tymbal acts as major determinant of the song radiating system via the elastic strain of the tymbal followed by frequency. The tymbal also acts as a frequency multiplier that the release as each tymbal rib buckles. The tymbal muscle has converts the 117 Hz contraction frequency of each of the paired no muscular antagonist, so re-extension of the muscle is brought tymbal muscles into the 4.3 kHz frequency of the insect’s song about by the elastic strain energy in the buckled tymbal. (Bennet-Clark, 1997; also see Michelsen, 1983, for a general Initially, the inward movement is opposed by the convex discussion of the role of frequency multipliers in sound tymbal ribs. As the tymbal plate is pulled in further, the tymbal production.) 1804 H. C. BENNET-CLARK AND A. G. DAWS

In many cicadas, the transduction of sound from mechanical and have been essentially qualitative. However, as the energy into acoustic energy takes place in distinct stages. transduction process from muscle power to acoustic power in During the first stage, the pulses of sound produced by the this cicada occurs in a comparatively small number of stages, tymbals cause high-pressure acoustic vibrations within the it is feasible to examine the energetics of transduction of abdominal air sac. The abdominal air sac and the large thin mechanical power to sound power. An earlier attempt to do eardrums of C. australasiae form, respectively, the compliant this with the mole Gryllotalpa vineae (Bennet-Clark, and inertial elements of a Helmholtz resonator tuned to the 1970) suffered from uncertainty about the available muscle song frequency (Young, 1990; Bennet-Clark and Young, power, but nonetheless suggested that the efficiency of 1992). This second stage in the transduction chain maintains transduction was remarkably high. the purity of the song and assists in producing a smooth song The insect used here is particularly suitable for energetic pulse envelope. Because the eardrums are far larger than the studies of this type. It is large and robust, and the sound is tymbals, this second stage also acts as an acoustic impedance produced as a long series of similar discrete pulses, each of converter between the tymbals and the surrounding medium which is produced by a single muscle contraction, in contrast (Bennet-Clark and Young, 1992; Bennet-Clark, 1995). with the songs of many other singing insects such as crickets In C. australasiae, the tymbal has four ribs (Fig. 1). As each (Popov et al., 1974) or cicadas (e.g. Fonseca, 1991) in which rib buckles, it converts a comparatively slow muscle far greater inter- and intra-pulse variability occur. Also, many contraction into a brief sound pulse. Each of these sound pulses elements in the sound-producing chain of Cyclochila has maximum amplitude in the first cycle and thereafter decays australasiae have now been studied (Bennet-Clark, 1997; exponentially (Bennet-Clark, 1997). This suggests that the Bennet-Clark and Young, 1992; Josephson and Young, 1981; tymbal acts as an energy storage/release mechanism which Young, 1990; Young and Bennet-Clark, 1995). provides an impulse that starts the sympathetic vibration of an The present work examines the energetics of various stages abdominal Helmholtz resonator (Young and Bennet-Clark, in the sound-production chain of the cicada C. australasiae: 1995). the tymbal muscle, the tymbal buckling process and the sound The action of the tymbal muscle on the tymbal can be power that is produced. modelled either by pulling on its apodeme or by pushing on its insertion on the tymbal plate (Simmons and Young, 1978; Bennet-Clark, 1997). Previous studies have been concerned Materials and methods with the nature of the sound produced as the tymbal buckled Insects and preparations Male Cyclochila australasiae Donovan were caught at night in parkland in Melbourne, Australia, as they emerged from the Axial last larval . Thereafter, they were kept in fine mesh bags Resilin push on a tree outside the Zoology Department of Melbourne pad Probe University or on acacia shrubs in the laboratory. In these rod regimens, they survived for over 2 weeks. Insects were used for experiments between 4 days and 2 weeks after eclosion; Apodeme only those that produced loud protest song when handled were Long pit used. ribs For most experiments, insects were prepared by removing the legs and wings, and then waxing the body to a 6 mm Resilin diameter support rod by the pro- and mesonotum. In addition, hinge for force and distance measurements, the body was made stiffer by waxing the first abdominal tergite to the metanotum and the Tymbal second abdominal sternite to the opercula on the thoracic plate metasternum using a 5 mm length of femoral cuticle. Singing was induced by brain stimulation via a pair of 0.1 mm diameter stainless-steel insect pins inserted into the front of the head 2 mm either side of the mid-line and 45 ¡ above the horizontal plane. Sound production was then induced Anterior ventral by short trains of 1 ms duration stimuli at 50 Hz and 2Ð5 V amplitude. Insects were mounted head up and, to stretch the abdomen and open the opercula to simulate the position found 2 mm in singing insects, a 20 g weight was suspended on a 50 mm Fig. 1. The tymbal of Cyclochila australasiae showing the tymbal length of wire waxed to the posterior end of the abdomen. plate and the sclerotised tymbal ribs. The drawing shows where the For force measurements on the tymbals, insects were killed probe rod of the stiff force transducer (see Fig. 2) was pushed against by placing them in a freezer at −15 ¡C for 30 min and then the apodeme pit on the tymbal plate. thawing them immediately prior to use. This procedure Energetics of cicada sound production 1805

A B Ferrite Probe rod Linear Hall Ferrite Probe rod magnet effect sensor magnet 0.15 mm Foil strain Foil strain thick steel gauges gauges springs

Silicone rubber

Veroboard terminal block

2.3 mm diameter aluminium tube Steel U-shaped Hook for Fig. 2. Diagrams of the front (A) and support calibration side (B) views of the stiff force weights transducer used to measure the Screened forceÐdistance relationships of leads tymbal buckling. The construction 6 mm diameter and characteristics of this transducer support rod are described in the text. 10 mm effectively detached the tymbal muscle from its apodeme and of the two outer faces of the steel shims (Fig. 2). These four sternal origin and also made it easy to dissect out the tymbal strain gauges were connected as a Wheatstone bridge. muscles for weighing. The stiff transducer was used to apply force to the tymbal via a probe rod glued into one end of the aluminium tube Tymbal muscle dimensions and trajectory that connected the springs on either side of the gauge. A The area of the tymbal muscle insertion on its apodeme (see hook for attachment of calibration weights was attached to Fig. 3C) was measured from camera lucida drawings using a the other end of this tube. As the effective mass of the tymbal Zeiss MOP digital measuring table. Muscle fibre lengths were is less than 1 mg (Bennet-Clark, 1997), the loading of the measured directly from the intact insect using Mitutoyo digital 0.5 g mass of the force transducer by the tymbal was callipers. negligible. The compliance of this transducer was Tymbal muscles were weighed to the nearest 0.1 mg after 49 µmN−1, which was approximately one-twentieth of that dissection from the previously frozen insect. Weighings were of the tymbals. Force could be resolved to 0.01 N at 200 Hz completed within 5 min of the start of the dissection. with linearity and cross-talk from side loads of better than The trajectory of the tymbal muscle fibres was measured 2%. from photographs of the abdomen, taken from behind after The distance moved by the probe rod of the force transducer removal of the posterior end or from the mid-line after splitting was measured using a UGN 3503 linear Hall effect sensor the insect’s body along the sagittal plane. The angle of the placed 0.5 mm away from a permanent magnet with a flat face tymbal muscle apodeme was measured from dissections of 2.5 mm high and 4.5 mm wide glued to the tube that held the dried specimens. probe rod (Fig. 2). The distance could be measured to ±5 µm over a range of 1 mm. According to the makers’ specification, Force and distance transducers the bandwidth of the distance sensor was from direct current Because the available commercial force and distance to over 10 kHz. transducers were unsuitable, special transducers were built, A more compliant force transducer with a resonant tested and calibrated. frequency of 100 Hz was constructed for measuring the force Measurements of the forceÐdistance relationships of the and distance relationships of the tymbal muscle. Its tymbal were made using a stiff transducer with a resonant compliance, 990 µmN−1, was similar to that of a typical cicada frequency of 1 kHz (Fig. 2). The springs were 20 mm lengths tymbal (see Fig. 8). Its sensitivity, its force and distance of 12.5 mm wide by 0.15 mm thick stainless-steel shim glued resolution and its linearity were similar to those of the stiffer with Sylastic silicone rubber to either side of a 12 mm high U- transducer. This compliant transducer was used as an elastic shaped steel support. Two Showa F8 foil strain gauges were load into which the tymbal muscle contracted; this type of glued with cyanoacrylate adhesive to the central parts of each auxotonic loading has been used to measure the forceÐdistance 1806 H. C. BENNET-CLARK AND A. G. DAWS relationships of flight muscle (Neville, 1965; Neville plotted using the MacChart or MacScope software; these loops and Weis-Fogh, 1963). were highly consistent (see Fig. 6). Both the force and distance transducers, as well as the At the end of each series of measurements, the angle of the preparation, were mounted on short 6 mm diameter brass probe rod was changed by 10 ¡ relative to the coordinates of or light alloy rods clamped in specially machined the insect body, and another series of measurements was made. holders bolted to the Prior micromanipulators. All In most cases, 10 measurements were made at 200 samples s−1 micromanipulators were mounted as close as possible to a followed by a further 10 at 1 kilosample s−1. Some 12 mm thick machined-steel baseplate using magnetic measurements were also made using MacScope to provide stands. Tests in which a force of 1 N was applied across the greater temporal resolution. apparatus showed that the movement between the end supports was less than 10 µm. Measurements of muscle contractions Stepwise force calibrations using weights and stepwise Tymbal muscle preparations were used in situ and as far as distance calibrations were carried out during every experiment, possible in their normal orientation. Using a live and also provided a test of the linearity of the response of the prepared for brain stimulation, a stainless-steel wire stirrup was apparatus. attached with cyanoacrylate glue to the outside of the tymbal plate, with the centre of the stirrup set to pull along the line of Data collection and analysis the tymbal apodeme. After the glue had set, a ring of cuticle One force transducer was connected to a MacLab bridge was cut away round the stirrup, detaching the apodeme and amplifier with a bandwidth of 2 kHz. stirrup from the tymbal. The stirrup was then connected to a Most force and distance data were recorded on separate force transducer via a 20 mm long loop of 0.3 mm diameter channels of an Analog Digital Instruments MacLab 4 12-bit stainless-steel wire. data-acquisition system using Chart 3.5 software at up to Force and distance measurements were made using the more 1000 samples s−1 with the channels sampled alternately, not compliant force transducer. Muscle contraction was elicited by simultaneously. Some forceÐdistance measurements were also brain stimulation (as described above): typically, a brief stimulus made using Scope 3.5 software at sampling rates of 4 or resulted in a train of between 5 and 20 muscle contractions. 10 kilosamples s−1. The temperature of the preparation was measured using a The software allowed baselines and scales to be defined. 0.2 mm diameter thermocouple placed inside the abdominal air Using the xÐy display, force versus distance work loops were sac of the cicada. The thermocouple was connected to a Bailey calculated directly. The work done or released was then 12 thermometer. The insect’s internal body temperature obtained as the area under different regions of the work loops. was raised from the ambient temperature of 24Ð25 ¡C to a maximum of 39 ¡C using a 60 W bench lamp. Repeat Measurements of the forceÐdistance relationships of tymbal experiments at 28 ¡C before and after heating to 39 ¡C buckling produced closely similar force and distance recordings. The insect preparation was mounted on one micromanipulator with its long axis parallel to the baseplate. Measurements of the sound field around the singing insect The stiff force transducer (Fig. 2) was mounted on another Sound pressure levels were measured using a Bruel and micromanipulator with its probe rod also parallel to the Kjaer 2230 sound level meter and Bruel and Kjaer 4155 baseplate. Using one protractor placed on the rod on which the microphone. The sound level meter was set to measure the insect was mounted and another on the baseplate, the position impulse peak maximum of the sound (which, for a continuous of the insect could be adjusted so that the angle of push on the pure-tone signal, is 3 dB higher than the root mean square value tymbal plate could be varied from 110 ¡ to a practical that is normally quoted as the sound pressure level). maximum of 170 ¡ above the mid-ventral line of the insect and Checks on the validity of the readings obtained were carried from 90 to 120 ¡ relative to the anterior-to-posterior long axis out as follows. The 1 kHz waveform produced by a Bruel and position (0 ¡ by 0 ¡ was taken as mid-ventral and anterior: see Kjaer type 4230 calibrator, giving 94 dB root mean square Figs 3A,B, 11). The precision of these settings was less than sound pressure, was recorded via the alternating current output ±3 ¡. socket of the sound level meter using MacScope. The peak After the force and distance transducers had been zeroed, the voltage of this recording was then compared with the peak insect was brought towards the probe rod of the force voltage of recordings of the insect sounds produced by brain transducer until contact was detected as a positive force stimulation. This procedure gave values that were within transducer reading. The vertical and horizontal positions of the 0.2 dB of those shown by the sound level meter. insect were adjusted so that the tip of the probe rod entered the The microphone was positioned 100±1 mm from the ventral apodeme pit on the tymbal plate (Figs 1, 3C). Force and surface of the insect at the opening of the tympanal opercula. distance recordings were then made as the probe rod was The insect was rotated in a series of 45 ¡ steps, first around the moved forwards and backwards rapidly over a distance of transverse plane, then in planes 45 ¡ anterior and 45 ¡ posterior 0.5Ð0.8 mm; with practice, the complete inÐout movement was to the transverse plane, and finally readings were taken 100 mm achieved in 0.3Ð0.4 s. Force versus distance loops were then straight in front of and behind the insect on the long axis. After Energetics of cicada sound production 1807 a set of readings around the insect had been completed, a pressure level of 90 dB (equivalent to a sound intensity of further set of readings was taken with the microphone in the 10−3 Wm−2) using the following equation: starting position to check that the insect was still producing the range = 10[(dB measurement − 90)/20] × 0.1 . (1) same sound level. The preparation was placed above an 85 mm thick sheet of These ranges were then used to draw 90 dB isobars of the Sonex anechoic foam. Further sheets of foam were inserted sound field. between the preparation and the support stands, and around the Calculations of the ratio of peak to mean power in the song sides and over the top of the preparation. There was no evidence were made from field recordings of singing cicadas made in of echoes in our recordings of song made in these conditions. 1988 by D. Young, using a Nagra IVS tape recorder and Five sound pressure measurements at 0.1 m range were Sennheiser MKH816 microphone. Portions of song taken at each position. The highest of these measurements was containing two or complete three sound pulses were recorded converted to the equivalent range (in m) for a peak sound onto MacScope at 100 kilosamples s−1. Pulse period was

Tymbal A 65¡ 110¡ Flight muscles muscle Tymbal apodeme Abdominal air sac Head

0¡ 180¡

Fig. 3. (AÐC) Drawings of the anatomy of Cyclochila australasiae to Chitinous V show the tymbal and tymbal muscles. 10 mm (A) Side view, with the anterior part of Operculum the abdomen cut away to the mid line, B to show the shape of the tymbal C muscle, its origin and its insertion; the Dorsal 180¡ Abdominal Anterior dashed lines show the angles of the 165¡ air sac muscle fibres relative to the horizontal Thorax plane (labelled 0 ¡ and 180 ¡). 152¡ Tymbal (B) Posterior view of the first apodeme Tymbal abdominal segment to show the shape Tymbal apodeme of the tymbal muscles, their origins on muscle the chitinous V and their insertions on Apodeme the tymbal apodemes. The dashed lines Tymbal pit on show the angles of the muscle fibres with ribs ABCD tymbal relative to the sagittal plane (labelled plate 0 ¡ and 180 ¡). (C) Dorsal view of the Operculum posterior end of the thorax and anterior 0¡ Tympanum Tymbal end of the abdomen, with the dorsal Ventral Base of chitinous V Abdomen muscle cuticle cut away to show the tymbals and tymbal muscles. Part of the dorsal 10 mm Posterior cuticle and tymbal have been cut away on the right side to show the tymbal 0¡ apodeme and the dorsal end of the D 180¡ 155¡ E Apodeme tymbal muscle. B and C are drawn to Apodeme the same scale. (D,E) Diagrams 20¡ 50¡ corresponding to B and C to show the 45¡ angles at which the strap-like region of the tymbal apodeme meets the Tymbal apodeme pit on the tymbal plate plate (shown as circles). In D, the tymbal Tymbal 45¡ 180¡ plate is shown as a vertical section and plate in E as a horizontal section, both 0¡ drawn through the apodeme pit. 1808 H. C. BENNET-CLARK AND A. G. DAWS measured from the MacScope recordings and used to obtain Results pulse frequency. Pulse duration was taken as the time from The anatomy of the tymbal and its muscle the start of the pulse to its decay to 10 dB below the peak The anatomy of the tymbal of C. australasiae has been level (Fig. 4A). The mean sound intensity of the pulses was described previously in some detail (Young and Bennet-Clark, calculated from the same recordings, following the procedure 1995; Bennet-Clark, 1997) (Fig. 1). The tymbal muscle inserts described below and illustrated in Fig. 4B. (This method of on the apodeme, which is connected to the tymbal plate via a calculating mean sound intensity is similar to that used in short flexible strap-like length of the apodeme (Fig. 3C). The Bennet-Clark, 1970.) (1) The sound level meter reading (in dorsal region on the tymbal plate from which the tymbal apodeme dB at 100 mm range) gave the amplitude of the loudest cycle invaginates forms a discrete pit approximately 0.15 mm in in the song pulse as a sound pressure (as given by the peak diameter. This apodeme pit acts as the focus for the force impulse reading). (2) A digitised oscillogram of two pulses produced by the tymbal muscle and also forms a convenient site of song was made (see Fig. 4A). (3) The data from stage 2 for external application of force via a probe rod (Fig. 1). were squared (see Fig. 4B). (4) The mean of the data set The tymbal muscle consists of a bundle of long fibres which obtained in stage 3 was calculated (this gives a relative extend from the sternal origin to their insertion on the tymbal measure of the mean sound power in the pulse). (5) The ratio apodeme. At the ventral origin on the chitinous V of the first of the mean value of the sound power to the square of the abdominal sternite (Fig. 3B,C), the cross section of the muscle amplitude of the largest cycle in the pulse was calculated (the is approximately oblong, but the cross section becomes amplitude of the largest cycle is obtained from stage 3). approximately circular at the tymbal apodeme (Fig. 3C). The Stages 2Ð5 were all calculated by the MacScope software. (6) muscle has the following measurements (mean ± S.D.): muscle The fractional peak power to mean power ratio was converted mass 87.1±14.3 mg (N=10); muscle fibre length 7.59±0.37 mm into a ratio in dB (a power ratio of 10:1=10 dB). (7) The mean (N=8); and apodeme insertion area 13.0±1.77 mm2 (N=7). sound intensity, integrated thoughout the pulse (in dB) was Viewed from normal to the sagittal plane (Fig. 3A), the obtained by subtraction of the values obtained in stages 1 and fibres form a truncated triangle which is broader at the ventral −2 6. 90 dB is a sound intensity of 1 mW m equivalent, in a origin of the muscle on the chitinous V. The most anterior −2 plane wave, to a sound pressure of 0.63 N m . (8) The mean fibres run upwards and backwards at 110 ¡ to the animal’s mid- sound intensity at 100 mm was converted to the range to a ventral line, and the most posterior run upwards and forwards 90 dB isobar using equation 1. (9) The mean sound power in at 60Ð65 ¡ to the mid-ventral line, with the centre of the muscle the song (in mW) is given by the area of the 90 dB isobar (in m2). A The total surface area of the sound field of the three- 2 Pulse dimensional map that was built up was then used to calculate duration the peak sound power output of the insects. This was converted 1 to an estimate of the mean power output using the peak power 0 to mean power ratio obtained for field records of calling song (see Table 2). -1 Relative sound Pulse period pressure level (V) Although our sound level measurements were recorded to -2 the nearest 0.1 dB or ±2.4 %, the realisable precision of these 2 ms Peak power 1.60 V2 measurements is unlikely to be better than ±0.5 dB or ±12 % 2 B ) because of inaccuracies in other parts of the measuring chain. 2 Mean power 0.202 V2 1 Terminology and conventions Relative Sound pressure levels are quoted throughout this study power (V 0 in decibels (dB) relative to the accepted threshold: 0 dB= Peak power to mean power ratio = 7.92:1 (9.0 dB) 20×10−6 Nm−2 (or relative to 20 µPa). This sound pressure level is equivalent, in the plane wave conditions that prevail here, to Fig. 4. The calling song of Cyclochila australasiae. (A) Oscillogram of a sound intensity (power per unit area) of 10−12 Wm−2. two pulses of song, recorded in the field, showing the terminology used Relative power is measured on a logarithmic scale in to define the components of the song: pulse duration is taken as the time decibels. 10 dB is a 10-fold power ratio (=101). A 1 dB from the start of the pulse to its decay to 10dB below the peak level. ratio=100.1 or a power ratio of 1.26. Sound power is The oscillogram shows relative sound pressure, as the output voltage of proportional to the square of sound pressure level. Therefore, the tape recorder, versus time. (B) Oscillogram of the relative power in the two song pulses shown in A. The voltages shown in A have been a 10 dB power (or sound intensity) ratio is equivalent to a 2 √ squared, and the ratio between the peak and mean values of (voltage) sound pressure ratio of 10 or 3.16. Whether the power ratio has been calculated for the two song pulses illustrated in A, both as a − is multiplicative or divisive is indicated by the sign: 3dB or ratio and as a relative ratio in dB. These calculations followed the − ‘3 dB below’ indicates a power ratio of 10 0.3 (1:0.5) or half procedure explained in steps 2Ð6 of the section of Materials and power. For a fuller discussion of these relationships, see Olson methods entitled Measurements of the sound field around the singing (1957) or Fletcher (1992). insect. The recordings were made at 100kilosampless−1. Energetics of cicada sound production 1809

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

Variable Mean±S.D. Range Maximum force at buckling (N) 0.38±0.08 0.28Ð0.55 Distance to buckling (µm) 368±84 300Ð620 Force decrease when rib 1 has buckled (N) 0.09±0.03 0.06Ð0.13 Residual force after all ribs have buckled (N) 0.17±0.04 0.10Ð0.25 Total energy in work loop (µJ) 75.5±27.5 43.5 to 119 Energy released by buckling of rib 1 (µJ) 16.5±7.5 8.8Ð28.2 Energy released by buckling of all ribs (µJ) 45.1±18.6 20.1Ð74.2 Energy available for outward movement (µJ) 32.8±12.2 18.3Ð56.7

N=11, except for the force decrease and energy release from the buckling of rib 1 where N=6. block running at approximately 85 ¡. Viewed from behind (Fig. inward movement were affected both by the position of the 3B), the fibres of the tymbal muscles run from close to the probe rod on the tymbal plate relative to the apodeme pit and midline at their ventral origins to their dorso-lateral insertions by the angle or direction of the push of the probe rod. on the tymbal apodemes at angles between approximately Because the tymbal muscle pulls in a linear manner via its 152 ¡ and 165 ¡ to the mid-ventral line, with the centre of the apodeme on the apodeme pit on the tymbal plate (Fig. 1) along muscle block running at approximately 160 ¡ to the mid-ventral the main trajectory of the muscle (Fig. 3), we tested the effect line. of changing both the position on the tymbal plate and the angle Viewed from the posterior, the dorsal regions of the tymbal at the apodeme pit at which force was applied by the probe rod. plates lie at an angle of approximately 20 ¡ either side of the The effect of moving the probe rod vertically on the tymbal sagittal plane. The strap-like distal part of the apodeme of the plate from 0.4 mm dorsal to the pit (the dorsal edge of the tymbal muscle, which is aligned with the central axis of the tymbal plate) via the apodeme pit to 2 mm ventral to the tymbal muscle, meets the tymbal plate at approximately 155 ¡ apodeme pit is shown in Fig. 5A for a push approximately to the sagittal plane and thus at approximately 45 ¡ to the dorso- normal to the surface of the tymbal plate, at 120 ¡ behind the ventral axis of the tymbal plate (Fig. 3D). Viewed from above, insect’s anterior in the horizontal plane and 140 ¡ above the the tymbal plates lie at angles of approximately 45 ¡ either side mid-ventral line in the sagittal plane. Both the force required of the insect’s long axis, and the strap-like regions of the and the distance through which the probe rod had to be moved apodemes run at 95 ¡ to the long axis, meeting the tymbal plates to bring about tymbal buckling were maximal when the tip of at approximately 50 ¡ to the horizontal axis of the plate the probe rod was positioned in the apodeme pit. (Fig. 3E). Taking the angles of 45 ¡ to the dorso-ventral axis The work required to bring about inward buckling of the and 50 ¡ to the horizontal axis of the tymbal plate, we calculate, tymbal, assuming that the tymbal obeys Hooke’s law (see by simple trigonometry, that the apodeme runs at an angle of Figs 6, 7), is given by 0.5 (force at buckling × distance at approximately 36 ¡ to the plane of the tymbal plate. buckling). Fig. 5A shows that the work required was maximal when the tymbal plate was pushed inwards at the apodeme pit, The effect of altering the position and direction of the applied but that only one-tenth as much work was required when the force tymbal plate was pushed inwards 2 mm ventral to the apodeme The force required to push the tymbal plate inwards rises pit. steadily until, suddenly, the tymbal ribs buckle inwards, The effect of altering the angle of push on the apodeme pit releasing energy. The forceÐdistance relationships of the is shown in Fig. 5B. It was difficult to make measurements at

Table 2. Characteristics of the calling song of Cyclochila australasiae

Variable Mean ± S.D. Range Pulse frequency (Hz)* 234±10.9 220Ð255 Pulse period (ms) 4.27±0.19 3.92Ð4.54 Pulse duration (ms) 2.47±0.46 1.43Ð3.09 (see Fig. 4A) Duty factor, pulse duration:pulse period 0.57±0.11 0.32Ð0.74 Peak power to mean power ratio 8.51±1.70:1 5.12Ð12.6 Peak power relative to mean power (dB) +9.30±0.90 7.09Ð11.0

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. 1810 H. C. BENNET-CLARK AND A. G. DAWS

A 0.5 Rib 1 in 0.4 500 100 1 Do Apodeme m) 0.4 2 3 J) pit µ µ Inwards 0.3 400 80 Rib 2 in 0.3 Ribs 0.2

Force (N) Ribs out Tymbal 300 60 plate 0.1 6 0.2 Ve Outwards 0 200 40 5 4 Distance -200 0 200 400 600 800 0.1 Distance strained (µm) Force 100 20 At pit Fig. 6. Force versus distance work loops for one tymbal of Distance moved before buckling (

Force required to buckle tymbal (N) Work Cyclochila australasiae. In this plot, ten successive loops are Work required to buckle tymbal ( 0 0 0 superimposed to show the repeatability of the measurements. The 3 2 1 0 1 Ventral Dorsal arrows show the direction of the work loops. The numbered stages of Position of push the inÐout movement described in the text are shown here by on tymbal plate (mm) numbers 1Ð6. Recorded at 1000 samples s−1.

0.6 B m) µ 600 tymbal plate after changing the angle of the probe rod. However, the same general trend was observed with 10 Force 0.4 tymbals: the force required to cause buckling and the distance 400 through which the probe rod had to be moved before buckling φ occurred both approximately doubled as the angle of push was increased from 110 ¡ to 170 ¡ above the mid-ventral line. This 0.2 200 is shown for one tymbal in Fig. 5B. The effect of altering the direction of push relative to the insect’s anterior–posterior axis Distance 0° was less marked (results not shown).

Force required to buckle tymbal (N) 0 0

90 120 150 180 Distance moved before buckling ( Energy storage and release by the tymbal Angle of push above mid-ventral, φ (degrees) The force required to move the tymbal plate inwards Fig. 5. Effects of altering the position and angle of push on the force increased steadily as the tymbal plate was pushed, until the versus distance relationships of tymbal buckling in Cyclochila tymbal ribs buckled (Figs 6, 7), when the force fell rapidly to australasiae. (A) Graph showing the force, distance and work less than half its peak value. Further inward movement was required to cause tymbal buckling when pushed at the apodeme pit or accompanied by a further increase in the force. As the probe at positions dorsal and ventral to the pit. In this preparation, the rod was withdrawn, the force decreased more or less steadily, direction of the push was 120 ¡ behind the insect’s anterior and 140 ¡ increased slightly as the tymbal ribs clicked outwards, then above its mid-ventral line. The inset shows the positions of the points decreased again until the probe rod was removed from the at which the tymbal was pushed (filled circles), cited dorsally (Do) tymbal plate. For any one preparation, the work and ventrally (Ve) relative to the apodeme pit on the tymbal plate. (forceÐdistance) loops that were obtained were highly (B) The force and distance required to cause tymbal buckling when repeatable (Fig. 6). pushed at the apodeme pit at angles between 110 ¡ and 170 ¡ above In summary, the work loops contain the following stages the insect’s mid-ventral line at an angle in the horizontal plane that was 110 ¡ behind the insect’s anterior. The dotted line at 155 ¡ shows after contact between the probe rod and the apodeme pit: these the approximate angle of pull of the tymbal muscle apodeme. The are numbered on Fig. 6. (1) Energy is stored elastically during inset shows the angle of push relative to the insect’s mid-ventral line; the initial phase of the inward movement; during this phase, the conventions adopted here are also used in Figs 3 and 11. the force rises approximately linearly. (2) The force decreases in a stepwise fashion as successive tymbal ribs buckle inwards. (3) After all the ribs have buckled, further inward movement angles of push of over 170 ¡ to the mid-ventral line or at angles of the tymbal plate causes further elastic distortion of the of push anterior to the insect’s transverse plane because the tymbal. (4) The initial part of the outward movement of the probe rod tended to slip out of the apodeme pit. At angles of tymbal shows an elastic, but non-linear, release of the push of more than approximately 130 ¡ behind the insect’s remaining stored energy. (5) During the latter part of the anterior, the probe rod tended to be obstructed by the cuticle outward movement, the force increases as the tymbal ribs of the tymbal frame (see Fig. 3C). It also proved difficult to buckle outwards. (6) Finally, the force decreases to zero as the obtain consistent results, probably because of the difficulty of probe rod is removed from the tymbal plate. positioning the tip of the probe rod in the same place on the The course of the storage and release of energy is shown in Energetics of cicada sound production 1811 detail in Fig. 7 for one tymbal which was pushed at 150 ¡ above This initial phase of movement of the tymbal plate was the mid-ventral line and at 110 ¡ to the anterior. The time essentially elastic. Experiments in which the tymbal was course of the changes in force together with the distance moved pushed inwards and released over distances that allowed the inwards then outwards is shown in Fig. 7A, and the tymbal plate to return outwards before buckling had occurred forceÐdistance work loop is shown in Fig. 7B. The initial phase showed a force versus distance pattern that closely mirrored of energy storage for this particular tymbal was almost linear. that during the inward phase (Fig. 8). This suggests that, during Slightly concave and convex forceÐdistance curves were the first part of the inward movement that precedes rib recorded from other tymbals. Peak forces before tymbal buckling, the elastic surround (Fig. 1) acts as a simple spring buckling of between 0.28 and 0.55 N were recorded from 11 controlling the movement of the tymbal plate. tymbals (Table 1). Previous work has shown that tymbal buckling occurs in a series of steps as successive ribs buckle inwards (Simmons and Young, 1978; Young and Bennet-Clark, 1995; Bennet-Clark, A 1997). Typically, the inward buckling of the first two or three In Out 0.4 400 ribs occurred over a time span of 1Ð3 ms, each of which Force

m) produced a pulse of sound. 0.2 Distance 200 µ Buckling of the tymbal ribs was always accompanied by a

Force (N) decrease in force and thus a release of energy by the elastic 0 0 regions of the tymbal. In most cases, it was difficult to measure Distance ( the precise contribution of the buckling of each individual rib 0 20 40 -200 Time (ms) B 0.4 Rib 1 in A Energy Energy 0.4 In storage release Out 0.3 Rib 2 in In Rib Elastic 0.2 buckling 0.2 recovery Force (N) Force (N) Rib 3 in 0 0.1 0 100 200 300 400 500 600 Time (ms) 0 Ribs out B 0 200 400 0.5 Rib 1 in Distance strained (µm) Partial relaxation Rib 2 in C J 0.4 µ 0.4 and re-strain Rib 3 in Total energy 26 µJ 0.3 in cycle, 0.3 69 µJ Inward

Force (N) strain 0.2 µ 0.2

Force (N) 14.8 J 5.6 µJ 0.1 Energy released 46 0.1 23 µJ Compliance 800 µm N-1 0 0 0 200 400 600 0 200 400 Distance (µm) Distance strained (µm) Fig. 8. (A) Force versus time curve showing an inÐout movement Fig. 7. Force relationships and work loop of a tymbal. (A) The force that did not cause the tymbal ribs to buckle (0Ð300 ms) followed by applied (thin line) and distance moved (thick line) during a rapid in- an inward movement that caused the ribs to buckle (from 450 ms then-out movement of the probe rod. The force initially rises almost onwards). The arrows show the direction of movement of the probe linearly throughout the inward movement until the tymbal ribs rod. (B) Graph of force versus distance for the movement shown in buckle rapidly, then remains almost constant over most of the A, indicating that the partial elastic recoil and subsequent re-strain subsequent outward movement. Recorded at 1000 samples s−1. that occurred between 120 ms and 520 ms in A is essentially elastic. (B) The forceÐdistance work loop from A. The inset shows the Note, too, that in this preparation, the buckling of successive tymbal direction of the loop and the processes that occurred. (C) The work ribs can be seen. The arrows show the directions of the components loop in B is shown broken into its energy components. The energy of the trace. The dashed line has a slope equivalent to a compliance released by successive rib buckling is shown as separate cross- of 800 µmN−1. This trace was recorded at 4000 samples s−1 and, hatched regions, and the residual energy that is available for elastic because of limited recording time at this rate, only shows the inward- recovery of the tymbal and its muscle is shown stippled. going part of the tymbal movement. 1812 H. C. BENNET-CLARK AND A. G. DAWS

0.4 Energetics of the tymbal muscle The experiments reported below were carried out at the end of the season when fewer were available. The force, 0.3 distance and work output of the tymbal muscle were measured to determine whether these variables were compatible with the 0.2 mechanical properties of the tymbal. Preliminary results are

Force (N) presented here, although incomplete, because of their 0.1 relevance to our other findings. 56 µJ The activity of the tymbal muscles was recorded in response to contractions elicited by brain stimulation. In all cases, the 0 muscle contraction rate was lower than the rate of 117 Hz for 400 300 200 100 0 each muscle that occurs in calling song, but in three Distance shortened (µm) preparations we recorded rates of 75Ð80 Hz at 28 ¡C. Force and Fig. 9. Force versus distance shortened for a burst of contractions distance were recorded simultaneously: Fig. 9 shows an produced by a tymbal muscle at 29 ¡C after activation by brain example of the forceÐlength curves that were obtained with the stimulation. The x axis shows the distance shortened relative to the muscle driving the compliant force transducer. The mean value unstimulated length of the muscle. Five loops were measured at of the peak active force recorded from seven preparations was 10 000 samples s−1. The stippled area shows the work done by the 0.31±0.04 N (mean ± S.D.) and the mean change in length or muscle on the springs of the force transducer, which had a similar strain of the work loop was 295±41 µm. This force is compliance to that of the tymbal. comparable with the value of 0.295 N obtained by Josephson and Young (1981) using C. australasiae (using an area of 13 mm2 for the tymbal muscle apodeme) and the values for to the course of the release of energy, but Fig. 7B shows a work force per unit area cited by Josephson and Young (1981). The loop in which the stages of buckling can be distinguished. In mean distance of shortening obtained here is 3.9 % of the this example, the force fell to approximately two-thirds of the muscle fibre length. The total work produced by the maximum value as rib 1 buckled and then to approximately contraction of the muscle is given by the area of the half the maximum as rib 2 buckled. approximately triangular region below the ends of the The forceÐdistance relationships of the outward recovery lengthÐdistance plot (Fig. 9). The mean work was movement after buckling tended to be markedly non-linear 47.0±11.2 µJ (N=7) (mean ± S.D., range 30Ð61.3 µJ). (Figs 6, 7). In many cases, the force remained almost constant Note that the measurements of distance have assumed that for most of the movement but showed a small increase, near the body of the cicada does not move when force is produced the end of the movement, as the tymbal ribs buckled outwards. by the tymbal muscle. However, it is likely that a small, hard- The areas of the forceÐdistance loops give the energy stored to-measure, part of the inward pull by the tymbal muscle and dissipated in different stages of the inward and outward brought about an inward distortion of the cicada abdomen. movement. These areas and the associated storage and release of energy are shown for a typical forceÐdistance loop in Fig. 7C. Initially, the force rises until the first tymbal rib 0.8 becomes unstable and buckles inwards suddenly, with an accompanying rapid decrease in force and release of stored energy, followed in sequence by buckling of the other tymbal 0.6 ribs. Of the total 69 µJ energy stored during the initial inward 200 W kg-1 µ movement, approximately two-thirds (46 J) was dissipated as 0.4 150 W kg-1 the tymbal buckled inwards, leaving the remaining one-third Fig. 9 µ (23 J) available to re-extend the tymbal muscle and restore the work area 100 W kg-1 tymbal to its resting position with the ribs buckled outwards. 0.2 Range of forces and strains 50 W kg-1 Values for the forceÐdistance relationships of 11 tymbals are required to buckle tymbal given in Table 1. The forceÐdistance relationships and the

Force required to buckle tymbal (N) 0 work loops of the tymbal shown in Fig. 7 are taken from a 0 100 200 300 400 500 600 tymbal with properties close to the mean values reported in Strain at which tymbal buckling occurs (µm) Table 1. Note that the measurements of distance assumed that Fig. 10. The mass-specific power output that would bring about the body of the cicada did not move when force was applied buckling of tymbals of different mechanical properties. Tymbal to the tymbal plate. In reality, it is likely that a small, but hard- muscle mass is taken as 87 mg, and the contraction frequency is to-measure, part of the inward movements that we recorded 117 Hz. The circle shows the power produced by the muscle shown occurred as a result of distortion of the cicada abdomen. in Fig. 9, assuming a contraction rate of 117 Hz. The filled square Consequently, the distances and energy values reported in shows the means ±1 S.D.(N=7) of the force and distance that cause Table 1 are likely to be slight overestimates. tymbal buckling (see Table 1). Energetics of cicada sound production 1813

Fig. 11. (A) Polar plot of the sound distribution around ° A 0 B ° a Cyclochila australasiae in which singing was 0 315° 45° induced by brain stimulation. The plots show the radial Range to 90 dB distance from the tympanal opercula of the 90 dB isobar in mean sound pressure level isobar, plotted at 45 ¡ ° ° 0.8 m horizontal plane 270 90 intervals around the body, in both the horizontal (open circles, broken line) and transverse (filled squares, 0.4 m 270° 90° solid line) planes. The horizontal and transverse patterns are approximately circular: these are shown as 180° stippled circles, respectively 0.5 m radius concentric 180° with the open circle at the centre of the plot and Range to 90 dB isobar in ° ° 0.55 m radius centred at the central filled square. 225° 135° 90 270 (B) Diagrams of the body of the insect showing the transverse plane conventions used for the coordinates of the polar plots. 180° 0° Upper: in the horizontal plane, where 0 ¡ is taken as anterior. 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). The boxes show the symbols and the stipple patterns used for the equivalent circles.

Consequently, the distances shortened and the energy values structure of the song were calculated from oscillograms (see calculated above are likely to be underestimates. Fig. 4A for terminology) and are given in Table 2. The ratio We measured the effect of pre-stressing the muscle in three of peak power to mean power in the song waveform was preparations. Passive stresses of 0.6 N could be applied calculated according to stages 2Ð6 of the procedure laid out in reversibly. With passive stresses between 0.05 and 0.3 N, we Materials and methods and illustrated in Fig. 4B. found that the muscles produced forceÐdistance plots that were closely similar in shape and area; in other words, over this The sound field around the singing insect and the mean sound range of passive stresses, the muscle appeared to produce a power similar active stress over a similar distance of active Sound fields were measured around three insects in which shortening. With passive stresses less than 0.05 N or greater sound production was elicited by brain stimulation. The sound than 0.4 N, the active force became smaller. It thus appears that was loudest mid-ventrally and quietest along the body axis in the muscle can contract over a range of passive stresses and the horizontal plane either directly anterior or directly posterior lengths and still produce similar amounts of work per cycle of to the insect but, overall, the sound radiation pattern only contraction. showed a difference of 3 dB between the loudest and quietest In one preparation, raising the internal body temperature directions. from 27 to 39 ¡C caused the rate of activation and contraction These measurements were converted to give the effective of the muscle following brain stimulation to increase from 73 size of the 90 dB sound pressure isobar as if the insect were to 97 Hz. Extrapolating from these data, the contraction rate of producing normal calling song. The values for the peak 117 Hz observed during singing would require a muscle impulse maximum sound pressure that had been made at temperature of approximately 42 ¡C. This temperature is 100 mm range were converted first by subtraction of 9.2 dB to comparable to the temperatures of 41Ð45 ¡C recorded for the give the mean sound intensity at that range. This value then tymbal muscles of the cicada Okanagana vanduzeei during was used to calculate the range to 90 dB sound pressure isobars singing (Josephson and Young, 1985). (Fig. 11). The work areas we obtained from the tymbal muscles are For the example shown in Fig. 11, the 90 dB sound isobar broadly compatible with the work required for buckling of the (equivalent to an intensity of 1 mW m−2) is approximately tymbal (c.f. Fig. 9 and Table 1). Taking a mean muscle equivalent to an ellipsoid of radii 0.50 m×0.50 m×0.55 m. The contraction rate of 117 Hz during singing and a mean muscle surface area of this ellipsoid is 3.45 m2. Thus, the mean sound mass of 87 mg, we can calculate the specific muscle power that power output of this particular insect was 3.45 mW; estimates is required to buckle the tymbal. Fig. 10 shows how the force from two other insects were 3.15 mW and 7.0 mW. required for tymbal buckling and the inward strain of the The peak sound pressures we measured are comparable with tymbal equate with the mass-specific muscle power of the the values reported by Young (1990) for the same species. We tymbal muscle. From Fig. 10, it appears that the tymbal muscle found peak sound pressures of 116.2, 116.8 and 118.9 dB at must produce between 75 and 125 W kg−1 to account for the 100 mm range for the three animals for which we had complete observed performance. recordings. These are equivalent to 110.2Ð112.9 dB at 200 mm range. At 200 mm range, Young reported mean values of Mean-to-peak power ratio of the song 109.9 dB +1.8 or −2.3 dB (mean ± S.D., N=5) for the protest Using recordings of the calling song made in the field by D. song and 112.9 dB +2.9 or −4.4 dB (N=8) for the calling song Young, the structure of the songs of seven C. australasiae was of C. australasiae. The equivalent mean sound powers are measured and analysed. Variables describing the temporal 3.15 mW for the protest song and 5.1 mW for the calling song, 1814 H. C. BENNET-CLARK AND A. G. DAWS assuming the same radiation pattern as in the present study, comparatively little inward force will be applied to the tymbal suggesting that the sound powers we measured in response to ribs, which will only buckle inwards after the application of a brain stimulation may be approximately two-thirds of those large force on the tymbal plate. In the second case, there will obtained under natural conditions (or approximately 2 dB be a more direct effect on the tymbal ribs, which will buckle lower). inwards with a smaller force (Fig. 12A, lower right). We The energy in each song pulse is the mean sound power observed a similar relationship between the force and distance divided by the song pulse rate (14.7 µJ assuming a pulse rate required to cause buckling of the tymbal (Fig. 5A), which of 234 Hz, range 13.5Ð30 µJ in the present study and 13.5 µJ suggests that the tymbal is designed to maximise the amount and 21.5 µJ for protest song and calling song from Young, of energy that can be stored prior to energy release by buckling 1990). These values can be compared with the work released of the ribs. by the buckling of all tymbal ribs in each cycle of tymbal Now consider the effects of altering the angle at which the buckling (Fig. 7; Table 1) for which a mean value of 45.1 µJ force is applied to the tymbal plate. Extreme cases are when was obtained, which is substantially greater than that the force is applied nearly parallel to the tymbal plate and when calculated for the song pulses. the force is applied nearly normal to the plate. In the first case, the turning moment will be small, but the distorting force acting on the resilin pad will be large; in the second case, the Discussion turning moment will be larger, and the distorting force acting The tymbal as a rapid-release energy-storage mechanism on the resilin pad will be smaller. These situations are modelled Mechanisms in insects by which energy is stored slowly and in Fig. 12B. The resultant force and distance required to cause released rapidly include the generation of sound pulses in buckling of the tymbal ribs were found to be smaller when the cicadas (Pringle, 1954) and moths (Blest et al., 1963) as well tymbal plate was pushed at angles close to the horizontal (or as the catapult mechanism of jumping fleas (Bennet-Clark and nearly normal to the plane of the tymbal plate) than when the Lucey, 1967) and many other fast-acting systems (for a review, angle of push was more nearly vertical and hence at an acute see Gronenberg, 1996). angle to the plane of the tymbal plate (Fig. 5B). Here, also, it Previous experiments have shown that the tymbals of appears that the elastic regions at the dorsal end of the tymbal cicadas produce discrete clicks of sound as the ribs buckle are designed to be distorted by the initial action of the tymbal inwards (Pringle, 1954; Simmons and Young, 1978; Bennet- muscle and thus to store energy for release by the buckling of Clark, 1997). The present work confirms these findings and the tymbal ribs. provides an energy budget for the elastic distortion of the The tymbal ribs, however, are light-weight, thin structures tymbal and the release of energy that accompanies the buckling (Young and Bennet-Clark, 1995; Bennet-Clark, 1997). of the tymbal ribs. Because buckling occurs approximately midway along their Previous work on the mechanical properties of the tymbal lengths (Fig. 12A), buckling requires that a far greater force be has shown that the thick resilin pad at the dorsal end of the applied at the dorsal ends of the ribs than is required at the tymbal (see Fig. 1) is a major elastic determinant of the points of buckling; thus, the ribs act as a trigger mechanism resonant properties of the tymbal (Bennet-Clark, 1997). The that is capable of retaining and then releasing large amounts of tymbal apodeme attaches close to the dorsal end of the tymbal stored energy. plate. The direction of pull along the apodeme is likely to cause The light weight and compliant nature of this trigger both an inward movement of the tymbal plate as a whole and mechanism ensure that the resonant properties of the tymbal also an inward distortion of the dorsal resilin pad. The tymbal will be dominated by the stiffness of the elastic elements of the plate can be modelled crudely as if it were a rigid lever pivoted tymbal and by the mass of the tymbal plate (which exceeds that at its dorsal end in the resilin pad; its inward movement is of the heaviest rib by a factor of five; Bennet-Clark, 1997); the opposed by the stiffness of the resilin pad and also by the lightness and compliance also ensure that the force required to resistance to buckling of the tymbal ribs. reset the trigger, by the buckling of the ribs back into their If this tymbal plate lever is pushed inwards (or pulled convex resting position, is far smaller than the force that must inwards by its muscle), the applied force will have two main be applied to the tymbal apodeme to bring about inward effects: to distort the resilin pad and to produce a turning buckling (Figs 6, 7), so the major part of the energy that is moment about the effective pivot. The response of such a stored in the elastic elements of the tymbal is available for system will be affected both by the position at which force is transduction into sound. applied and by the angle at which the force is applied. These are modelled in Fig. 12. The tymbal as a load and antagonist to a high-power muscle Consider two cases in which force is applied to different To fulfil its role in sound production, the tymbal should regions of the tymbal plate: first at the apodeme pit where the provide two types of loading to its muscle: it should store and force is applied close to the pivot; and, second, ventral to the then dissipate the major part of the work done in each cycle of apodeme pit, close to the region in which the tymbal ribs muscular contraction; it should also provide sufficient residual buckle (Fig. 12A). In the first case, a major effect will be strain energy to re-elongate the relaxing muscle. It seems likely distortion of the resilin pad (Fig. 12A, upper right) and that the major elastic energy store is the resilin pad (Fig. 1), Energetics of cicada sound production 1815

A Push at the apodeme pit Resilin pad Push stores energy by distortion of the resilin pad

Push nearer the region of rib buckling Small force acting where the tymbal ribs buckle

Region at which Fig. 12. Diagrams of the effects of pushing the tymbal Little energy is rib buckling occurs plate at various positions and angles. In the left-hand stored in the resilin diagrams, showing drawings of the tymbal, the direction pad of push is shown as lines in the plane of the plate, but the actual direction of push is assumed to be in a plane approximately normal to the plate. The right-hand Push acts close to diagrams show how the push at different positions or region at which rib from different directions acts on the tymbal. (A) A Long ribs buckling occurs comparison between the effect of pushing either at the apodeme pit or nearer to the region at which the tymbal ribs buckle. The tymbal plate is modelled as a lever suspended by and pivoting at the dorsal resilin pad (see Push at 36¡ to the Fig. 1). When force is applied at the apodeme pit (right B 0¡ upper), there is considerable distortion of the resilin pad plane of the tymbal 36¡ but little force is applied at the region of rib buckling. plate When force is applied closer to the region of rib buckling Applied force and (right lower), a relatively greater component of the force Push at 70¡ to the distance vector is applied to the tymbal ribs but a smaller component is plane of the tymbal applied to the resilin pad. The energy required for plate buckling of the tymbal is greater when the push is at the 70¡ apodeme pit than when the push is close to where the ribs 90¡ buckle (see Fig. 5A). (B) The effect of pushing at the apodeme pit at different angles to the plane of the tymbal Resultant force and plate (see Fig. 5B). When the angle of push runs distance vector normal obliquely to the tymbal plate (at 36 ¡), the component of to the tymbal plate the force vector acting normal to the tymbal plate will be relatively smaller than when the push runs more nearly normal to the tymbal plate (at 70 ¡). The force required to buckle the tymbal and the distance moved before Tymbal plate buckling will be greater with a 36 ¡ push than with a 70 ¡ push (see Fig. 5B). In the intact animal, the apodeme runs at an angle of approximately 36 ¡ to the plane of the tymbal (see Results and Fig. 3). which is a major determinant of the resonant frequency of the the loading provided by the tymbal may be very different tymbal (Bennet-Clark, 1997), but the highly stressed tymbal from the simple elastic load used here. In this context, it apodeme may also store a proportion of the muscle energy. The should be noted that the singing insect adjusts the position strap-like region of the apodeme is relatively short and thin so and dimensions of its abdominal resonator (Young, 1990), its contribution to the energetics of the tymbal cycle is presumably to exploit its muscle power maximally; it is also probably minor. able to alter the curvature of the tymbal, and presumably the The muscle contraction cycles described here suggest that work required to buckle it, by the activity of the tymbal tensor the muscle is capable of producing an appropriate force over muscle (Pringle, 1954; Fonseca and Hennig, 1996), which an appropriate distance to distort the tymbal to the stage at will have similar effects. which it buckles inwards (c.f. Figs 7C and 9). The probable power output from the muscle (Fig. 10) is approximately half The energetics of sound production the highest values reported for the sustained power output Sound production in a cicada such as C. australasiae occurs from striated muscle (see, for example, Weis-Fogh and as a series of links in a chain: a neural pattern initiates muscle Alexander, 1977; Askew and Marsh, 1997), suggesting that contraction; the muscle contractions are converted into 1816 H. C. BENNET-CLARK AND A. G. DAWS mechanical work; the mechanical work is transduced into The experimental work reported here was largely carried sound. out at the University of Melbourne. This work was supported From the measurements reported in the present study, we can in part by an Australian Research Council grant to Dr David derive approximate values for the energy involved in the last Young. We thank David Young for his support and two links of this chain. A typical muscle contraction through encouragement throughout this work, for the loan of space 0.30 mm produces a peak force of 0.32 N and thereby produces and equipment and for allowing us to analyse his song 47 µJ of energy: these values are broadly compatible with, records. This work was made possible by an Overseas Study although somewhat lower than, the mean values required to Visit Grant from the Royal Society to H.C.B.-C. and bring about tymbal buckling (Table 2). As the tymbal buckles, permission to take sabbatical leave from Oxford University it produces a train of pulses of increased air pressure within the and St Catherine’s College, Oxford; this generosity is abdominal air sac of the cicada, which excites and sustains a gratefully acknowledged. Special thanks are due once more to sympathetic resonance in the abdominal Helmholtz resonator the Department of Zoology, University of Melbourne, and to (Bennet-Clark and Young, 1992; Young and Bennet-Clark, Professor M. B. Renfree for hospitality throughout H.C.B-C’s 1995), from which sound is radiated via the large ventral stay in Australia, without which this work could not have tympana (Young, 1990) (see Fig. 3B,C). Each pulse of the song been undertaken. We also thank two anonymous referees for is produced by a single muscle contraction and consequent constructive comments on an early version of this paper. inward buckling of one of the two tymbals. The mean energy in a pulse of the calling song is 21.8 µJ and the mean energy released by the buckling of all tymbal ribs is 45.1 µJ, but both References these values show variations of approximately ±35 %. Askew, G. N. and Marsh, R. L. (1997). The effects of length Taking the mean values for the energy of tymbal buckling trajectory on the mechanical power output of mouse skeletal (47 µJ) and the energy per pulse of calling song (21.8 µJ), the muscles. J. Exp. Biol. 200, 3119Ð3131. efficiency of transduction from mechanical energy to sound Bennet-Clark, H. C. (1970). The mechanism and efficiency of sound energy appears to be approximately 46 %. Even using the production in mole crickets. J. Exp. Biol. 52, 619Ð652. maximum value for the energy that can be released by tymbal Bennet-Clark, H. C. (1995). Insect sound production: transduction buckling (74.2 µJ) and the lowest values for the energy per mechanisms and impedance matching. In Biological Fluid sound pulse (13.5 µJ) gives a transduction efficiency of 18 %. Dynamics (ed. C. P. Ellington and T. J. Pedley), pp. 199Ð218. The very high efficiency that we ascribe to the mechanical- Cambridge: Company of Biologists Ltd. Bennet-Clark, H. C. (1997). Tymbal mechanics and the control of to-sound transduction process is similar to that suggested for a song frequency in the cicada Cyclochila australasiae. J. Exp. Biol. similar process of transduction in the mole cricket Gryllotalpa 200, 1681Ð1694. vineae (Bennet-Clark, 1970). This efficiency is far higher than Bennet-Clark, H. C. and Lucey, E. C. A. (1967). The jump of the the overall efficiency of the whole animal reported for the flea: a study of the energetics and a model of the mechanism. J. sound production of Gryllotalpa australis and the cricket Exp. Biol. 47, 59Ð76. Teleogryllus commodus (Kavanagh, 1987), which was found Bennet-Clark, H. C. and Young, D. (1992). A model of the to be 1.05 % and 0.05 % respectively. This reflects the fact that mechanism of sound production in cicadas. J. Exp. Biol. 173, we are only examining the energetics of one or two links in the 123Ð153. chain, rather than the energetics of the whole animal, as Blest, A. D., Collett, T. S. and Pye, J. D. (1963). The generation of measured by Kavanagh (1987), which includes the energetics ultrasonic signals by a New World arctiid moth. Proc. R. Soc. Lond. of its physiological support systems. B 158, 196Ð207. Fletcher, N. H. (1992). Acoustic Systems in Biology. Oxford: Oxford Nonetheless, such a high apparent transduction efficiency University Press. deserves further comment. Although the tymbal provides the Fonseca, P. J. (1991). Characteristics of the acoustic signals in nine pressure drive to the abdominal resonator (Young and Bennet- species of cicadas (, ). Bioacoustics 3, Clark, 1995), the sound is radiated through the large tympana, 173Ð182. which are extremely thin (Young, 1990) and extend across the Fonseca, P. J. and Hennig, R. M. (1996). Phasic action of the tensor full width of the abdomen. As such, the tympana provide a muscle modulates the calling song in cicadas. J. Exp. Biol. 199, sound source that can be modelled as a piston in an infinite 1535Ð1544. baffle. The coupling of a sound source to the fluid medium into Gronenberg, W. (1996). Fast actions in small animals: springs and which it is radiating depends on the specific acoustic resistance click mechanisms. J. Comp. Physiol. 178, 727Ð734. of the source relative to that of the fluid medium (see, for Josephson, R. K. and Young, D. (1981). Synchronous and example, Olson, 1957; Fletcher, 1992). Calculations based on asynchronous muscles in cicadas. J. Exp. Biol. 91, 219Ð237. Josephson, R. K. and Young, D. (1985). A synchronous insect the dimensions of the tympana suggest that their specific muscle with an operating frequency greater than 500 Hz. J. Exp. acoustic resistance is close to that of the air into which they Biol. 118, 185Ð208. are radiating sound (Bennet-Clark, 1995). Thus, the extreme Kavanagh, M. W. (1987). The efficiency of sound production in two specialisation of the abdomen in male cicadas can be seen to cricket species, Gryllotalpa australis and Teleogryllus commodus result in efficient mechanical to sound energy transduction and, (Orthoptera: Grylloidea). J. Exp. Biol. 130, 107Ð119. for their size, the production of extremely loud sounds. Michelsen, A. (1983). Biophysical basis of sound communication. In Energetics of cicada sound production 1817

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