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Resonating Glass
Lisa Kastenhuber
scichallenge2017
1
Task
• A wine glass partially filled with liquid will resonate when
exposed to the sound of a loudspeaker. Investigate how
the phenomenon depends on various parameters.
2
3
Basic explanation
• Harmonic damped driven oscillator: sound excites glass
at resonance frequency
 Wine glass: resonance body, influenced by
• Glass itself: size, volume
• Liquid: amount of liquid, different liquids
Task: investigate resonance frequency
in dependency of wine glass parameters
A wine glass partially filled with liquid will resonate when exposed to
the sound of a loudspeaker. Investigate how the phenomenon depends
on various parameters.
4
Theoretical model
Assumptions: Harmonic, damped, driven osscillation
𝑚 𝑥 + 𝑏 𝑥 + 𝑐𝑥 = 𝐹sin(Ω𝑡)
𝑥 +
𝑏
𝑚
𝑥 +
𝑐
𝑚
𝑥 =
𝐹
𝑚
sin(Ω𝑡)
Harmonic: 𝜔 =
𝑐
𝑚
 eigenfrequency
Damping: 𝛿 =
𝑏
2𝑚
 friction: glass, air, liquid, amount of liquid
Driven: 𝐹𝑠𝑖𝑛(Ω𝑡)  loudspeaker: 𝐹 „amplitude“, Ω frequency
First experimental setup
5
Amplifier
Sine Generator
Stroboscope
Camera
Loudspeaker
Glass
Measuring
Glass
Visual data analysis
6Made with open source program „Tracker“
7
Improved experimental setup
Thanks to faculty of Engeneering of TU Munich
Laser
Glass
Reflector-Spray
Cellular
material
Signal-Decodor
Loudspeaker
Laptop
Data analysis
8Vibsoft 5.2.2 licence by TU Munich
Different resonance frequencies
9
0.00E+00
2.00E-07
4.00E-07
6.00E-07
8.00E-07
1.00E-06
1.20E-06
1.40E-06
0 1000 2000 3000 4000 5000 6000 7000
v/(m/s)
f/Hz
glass1_500ml_H2O
Two different frequencies
10
468Hz
470Hz
When you look at the
peaks on the slide
before more precious
you can see the glass
resonates at two
frequencies with a
difference of only 2 or 3
Hertz.
That is because the
glass is assymetric.
Interference of the oscillations
11
Parameter: amount of liquid
12
𝜔 =
𝑐
𝑚
390
400
410
420
430
440
450
460
470
480
0 50 100 150 200 250 300 350 400 450
resonancefrequencyinHz
filling in ml
glass 1
Glass parameters
-Different wine glasses
13
Glass 1 Glass 2 Glass 3
Whole height:
Total filling height:
Diameter upper glass:
Diameter glass wall:
0,227m
0,124m
0,068m
0,0006m
0,225m
0,109m
0,076m
0,0013m
0,197m
0,097m
0,026m
0.0008m
Parameter: different glasses
14
𝜔 =
𝑐
𝑚
350
400
450
500
550
600
650
700
750
0 100 200 300 400 500 600
resonancefrequencyinHz
filling in ml
different glasses
Glas 1 Glas 2 Glas 3
1
2
3
Calculation of resonance frequency
15
Simplification: glass as hollow cylinder
v = 𝑓λ =
π𝑢𝑓𝑑
3
1
2
λ = π𝑟
f =
𝑑𝑢
3π𝑟2
r = radius
f = frequency
λ = wavelength
u = sound velocity
d = thickness glass wall
Problem:  cylinder has a different form
 height is not exactly fixed
 filling is not included
http://www.ucke.de/christian/physik/ftp/lectures/
Glockenklang.pdf
Theory - Experiment - comparison
16
Simplification: glass as hollow cylinder
Frequency calculated:
Frequency meassured:
Glass 1 Glass 2 Glass 3
496Hz
468Hz
860Hz
586Hz
795Hz
715Hz
Damping – Parameter: liquid
17
Glass 1
100ml
WATER
468Hz
Glass 1
100ml
GLYCERIN
468Hz
𝛿 =
𝑏
2𝑚
Frequency: conclusion
18
Dependent on: glass itself, filling amount
Independent of: liquid
Conclusion
19
Multiple setups
Approximate analysis
𝑚 𝑥 + 𝑏 𝑥 + 𝑐𝑥 = 𝐹sin(Ω𝑡)
Theoretical model
Frequency
Dependent on: glass itself, filling volume
Independent of: liquid
Calculation of frequency
f =
𝑑𝑢
3π𝑟2
Thank you for your attention!
20

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#scichallenge2017 Resonating glass

  • 2. Task • A wine glass partially filled with liquid will resonate when exposed to the sound of a loudspeaker. Investigate how the phenomenon depends on various parameters. 2
  • 3. 3 Basic explanation • Harmonic damped driven oscillator: sound excites glass at resonance frequency  Wine glass: resonance body, influenced by • Glass itself: size, volume • Liquid: amount of liquid, different liquids Task: investigate resonance frequency in dependency of wine glass parameters A wine glass partially filled with liquid will resonate when exposed to the sound of a loudspeaker. Investigate how the phenomenon depends on various parameters.
  • 4. 4 Theoretical model Assumptions: Harmonic, damped, driven osscillation 𝑚 𝑥 + 𝑏 𝑥 + 𝑐𝑥 = 𝐹sin(Ω𝑡) 𝑥 + 𝑏 𝑚 𝑥 + 𝑐 𝑚 𝑥 = 𝐹 𝑚 sin(Ω𝑡) Harmonic: 𝜔 = 𝑐 𝑚  eigenfrequency Damping: 𝛿 = 𝑏 2𝑚  friction: glass, air, liquid, amount of liquid Driven: 𝐹𝑠𝑖𝑛(Ω𝑡)  loudspeaker: 𝐹 „amplitude“, Ω frequency
  • 5. First experimental setup 5 Amplifier Sine Generator Stroboscope Camera Loudspeaker Glass Measuring Glass
  • 6. Visual data analysis 6Made with open source program „Tracker“
  • 7. 7 Improved experimental setup Thanks to faculty of Engeneering of TU Munich Laser Glass Reflector-Spray Cellular material Signal-Decodor Loudspeaker Laptop
  • 8. Data analysis 8Vibsoft 5.2.2 licence by TU Munich
  • 10. Two different frequencies 10 468Hz 470Hz When you look at the peaks on the slide before more precious you can see the glass resonates at two frequencies with a difference of only 2 or 3 Hertz. That is because the glass is assymetric.
  • 11. Interference of the oscillations 11
  • 12. Parameter: amount of liquid 12 𝜔 = 𝑐 𝑚 390 400 410 420 430 440 450 460 470 480 0 50 100 150 200 250 300 350 400 450 resonancefrequencyinHz filling in ml glass 1
  • 13. Glass parameters -Different wine glasses 13 Glass 1 Glass 2 Glass 3 Whole height: Total filling height: Diameter upper glass: Diameter glass wall: 0,227m 0,124m 0,068m 0,0006m 0,225m 0,109m 0,076m 0,0013m 0,197m 0,097m 0,026m 0.0008m
  • 14. Parameter: different glasses 14 𝜔 = 𝑐 𝑚 350 400 450 500 550 600 650 700 750 0 100 200 300 400 500 600 resonancefrequencyinHz filling in ml different glasses Glas 1 Glas 2 Glas 3 1 2 3
  • 15. Calculation of resonance frequency 15 Simplification: glass as hollow cylinder v = 𝑓λ = π𝑢𝑓𝑑 3 1 2 λ = π𝑟 f = 𝑑𝑢 3π𝑟2 r = radius f = frequency λ = wavelength u = sound velocity d = thickness glass wall Problem:  cylinder has a different form  height is not exactly fixed  filling is not included http://www.ucke.de/christian/physik/ftp/lectures/ Glockenklang.pdf
  • 16. Theory - Experiment - comparison 16 Simplification: glass as hollow cylinder Frequency calculated: Frequency meassured: Glass 1 Glass 2 Glass 3 496Hz 468Hz 860Hz 586Hz 795Hz 715Hz
  • 17. Damping – Parameter: liquid 17 Glass 1 100ml WATER 468Hz Glass 1 100ml GLYCERIN 468Hz 𝛿 = 𝑏 2𝑚
  • 18. Frequency: conclusion 18 Dependent on: glass itself, filling amount Independent of: liquid
  • 19. Conclusion 19 Multiple setups Approximate analysis 𝑚 𝑥 + 𝑏 𝑥 + 𝑐𝑥 = 𝐹sin(Ω𝑡) Theoretical model Frequency Dependent on: glass itself, filling volume Independent of: liquid Calculation of frequency f = 𝑑𝑢 3π𝑟2
  • 20. Thank you for your attention! 20