7. Crickets Some insects, such as crickets, produce a rather impressive sound by rubbing together two parts of their body. Investigate this phenomenon. Build a device producing a sound in a similar way. Swiss Team, Seoul 2007

Overview 1. Theory 2. Model 3. Comparison cricket in reality/ model Wing resonances (Primary resonators) Burrows (Secondary resonators) Dimensions Typical acoustics 2. Model Our model cricket 3. Comparison cricket in reality/ model 4. Acknowledgements Swiss Team, Seoul 2007

Theory: Production of wing resonances Transduction of muscle energy into sound energy happens in two steps: 1. muscle power drives a small mechanical resonator (primary resonator) 2. larger acoustic resonator: louder sound → better impedance matching with air (secondary resonator) Crickets (e.g. acheta domesticus): 1. produce their sound by rubbing together their two forewings left wing „scratches“ with an edge on a file at the right wing → vibration → sound 2. build a burrow : same resonance as the sound they emit Our model simulates the primary resonator This drives a larger acoustic resonator to have a louder sound The left wing „scratches“ with an edge on a file at the right wing which leads to vibration and therewith to the sound Swiss Team, Seoul 2007

Theory: Primary resonator Basic principle: Left wing with left plectrum „scratches“ the right file on the underside of the right wing: system set in vibration. → file-and-plectrum mechanism right wing Source: H.C. Bennet-Clark, (4) left wing Swiss Team, Seoul 2007

Theory: Primary resonator Right file consists of about 250 teeth that are 20 μm tall Left plectrum has a 2 μm tip radius: engages the teeth left wing Source: H.C. Bennet-Clark, (3) Swiss Team, Seoul 2007

Theory: Primary resonator “scratching” of plectrum of left wing on file teeth on right wing leads to an oscillation with dominant frequency fD file teeth on right wing plectrum on left wing Source: H.C. Bennet-Clark, (4) Swiss Team, Seoul 2007

Theory: Primary resonator due to movement of file, some parts of the wing start to oscillate: harp (green) mirror (blue) → sound is produced (primary resonator) Mirror Harp Material der flügel file Source: H.C.Bennet Clark, (3) Swiss Team, Seoul 2007

Theory: Secondary resonator With help of a secondary resonator crickets increase the power of their signal: Subterranean burrow → Tuned to resonant frequency of sound-producing wings In the model we investigated the primary resonator (and did not look at the secondary resonators) Formel/berechnung für resonanzfrequen bei kugel mit bestimmtem radius: zeigen dass grösse und cricket zusammen passen Source: H.C. Bennet-Clark, (2) Swiss Team, Seoul 2007

Theory: Secondary resonator Order of magnitude: Spherical Helmholtz-resonator f=resonance frequency r=radius opening V=volume of the resonator f = 5 kHz r = 5 mm 0.5 cm 2cm Swiss Team, Seoul 2007

Dimensions We used acheta domesticus 4 – 6 cm long we put 7 males with 2 females together: only males chirp recorded their songs with microphones and acoustic analysing software Source: www.bioweb.com/index/anicri/cricket.jpg Swiss Team, Seoul 2007

Typical acoustics Song is made up of a series of trills with a variable number of pulses Swiss Team, Seoul 2007

Typical acoustics Frequency spectrum: Maxima at 4.8 kHz and 5.2 kHz: dominant frequencies very reasonable ( compared to literature: H.C. Bennet-Clark) Swiss Team, Seoul 2007

Experiment We built a device that produces sound in a similar way to crickets. Assumption: Goal: simulation of manner of sound production Mit bestimmter geschw: zähne anregen Flügel mit lautsprecher anregen Swiss Team, Seoul 2007

Experiment: setup Simulation of the file-and-plectrum mechanism: File plectrum Consists of ca 1400 teeth: 140 rows 0.2 mm tip radius Swiss Team, Seoul 2007

Experiment: setup Simulation of the harp (primary resonator) → by pulling the metal tip over the file we set the two metal plates (spring steel) into vibration Swiss Team, Seoul 2007

Experiment: setup Both plates fixed on one end → undisturbed oscillation Plate with metal tip is on a cart on a track and pulled by a motor → smooth movement The sound is recorded by a microphone and connected to analysing software microphone cart track Swiss Team, Seoul 2007

Comparison cricket/ device Primary resonator: Forewings rub each other Plectrum engages and releases teeth on file File sets harp and mirror into oscillation → sound waves are emitted device Metal tip scratches metal file with very small teeth File sets metal plates into oscillation → sound waves are emitted Swiss Team, Seoul 2007

Our device as a cricket left wing plectrum file right wing harp/mirror Swiss Team, Seoul 2007

Experiment: measured frequency Frequency: fmeasured = 41.5 Hz Swiss Team, Seoul 2007

Experiment: results Calculation of frequency (plate fixed on one end): L = length of plate E = Young‘s modulus h = height of plate ρ = density of material (spring steel) , Source: „The physics of musical instruments“ Swiss Team, Seoul 2007

Experiment: results Our device produced a trill similar to crickets Several pulses with decreasing amplitude Simulation of plectrum-and-file-mechanism works really well! Swiss Team, Seoul 2007

Experiment: results one pulse corresponds to one engagement our „plectrum“ does not engage every tooth it passes length of one pulse ≈ 5 teeth Swiss Team, Seoul 2007

Conclusions What we did: Our device fulfils all requirements! We recorded the sound of crickets We could investigate this sound We built a device producing the sound in a similar way We investigated our device Our device fulfils all requirements! Swiss Team, Seoul 2007

Acknowledgements Sources: H.C. Bennet-Clark, W.J. Bailey, N. H. Fletcher (Oxford University and University of Western Australia) (1) Resonators in insect sound production: how insects produce loud pure-tone songs (2) Acoustics of a small Australian burrowing cricket: the control of low-frequency pure-tone songs (3) Wing resonances in the Australian field cricket Teleogryllus oceanicus (4) Ticking of the clockwork cricket: the role of the escapement mechanism N.H. Fletcher, T.D. Rossing; The physics of musical instruments; Springer Verlag New York Inc.; 1991 Swiss Team, Seoul 2007