A wineglass partially filled with liquid will resonate when exposed to the sound of a loudspeaker. This Phenomenon must be investigated in dependency of different wineglass parameters.#scichallenge2017

1. Resonating Glass
Lisa Kastenhuber
scichallenge2017
1

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

9. 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

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
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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
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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
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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!
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