1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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:
Swiss Team, Seoul 2007

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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

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

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

20. 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

21. 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

22. 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

23. 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

24. 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