What Makes the Resonance Square Experiment a Unique Physics Demonstration?

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    Resonance Square
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Discussion Overview

The discussion centers around the uniqueness of the Resonance Square Experiment as a physics demonstration, particularly focusing on the wave functions involved and the observed resonance modes. Participants explore theoretical aspects, experimental observations, and the mathematical descriptions of the modes produced in the experiment.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants express interest in the experiment and its visual demonstration of wave functions.
  • One participant notes that the eigenmodes of the vibrating membrane are Bessel functions and discusses the behavior of sand settling in nodal lines, suggesting a comparison between theory and experiment.
  • Another participant introduces the idea that the modes observed in the demonstration are a blend of Bessel functions and Hermitian polynomials, attributing this to the combination of cartesian symmetry of the membrane and the rotational symmetry of the driving force.
  • There is a mention of a resource that provides further explanation of the modes involved in such experiments.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the nature of the resonance modes, with some agreeing on the presence of Bessel functions while others propose a more complex blending of modes. The discussion remains unresolved regarding the exact classification of the modes observed.

Contextual Notes

There is an implicit assumption about the definitions of eigenmodes and their mathematical representations, which may not be universally agreed upon. The discussion does not resolve the mathematical steps involved in identifying the modes.

Orion1
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I thought that this would be an interesting video for physics majors:
http://www.spikedhumor.com/articles/26352/Resonance_Square.html"

I posted it here, because the experiment appears to involve 'wave function'.
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Yeah, that's pretty cool. I've never seen such a demonstration live though (but that's okay, because here I can turn down the volume on my speakers).

IIRC the eigenmodes of such a vibration membrane are Bessel functions. The sand will be thrown away from the vibrating places and settle down in the nodal lines, which you can calculate. So by observing the shapes you can directly compare theory and experiment and see which resonance mode you have hit.
 
Here is a site which explains a bit about http://www.phy.davidson.edu/StuHome/jimn/Java/modes.html"
 
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That was freaking awesome!
 
Galileo said:
IIRC the eigenmodes of such a vibration membrane are Bessel functions.

Circular symmetry gives Bessel modes, while cartesian symmetry gives Hermitian modes.

The modes in the demonstration are not Bessel functions or Hermite polynomials, but an interesting blend of both. The blending possibly comes about because you have a membrane with cartesian symmetry, yet the driving force (speaker) is rotationally symmetric.

Claude.
 

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