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Physics investigation guidance: Vibration of circular plate

  1. Feb 10, 2015 #1
    Hi,

    I have previously made a post in order to gain some insight in my rather out of control project. Long story short I am investigating vibration of a circular plate and its standing waves. After consultation at this forum I have been guided in the direction of acoustics and bessel functions (which at the moment is a bit more than I can handle but due to the nature of my investigation it's something I just have to deal with).

    I can start off with explaining a bit more in-depth of what I have and what I want to achieve. I have conducted an experiment where I have a plate which is connected to a mechanical wave driver and a signal generator. Then after I have sprinkled sand over the plate and changed the frequency until I get circular nodal patterns. My problem now is that I'm having some difficulties how to deal with the information I now have. I have noted down all the frequencies in which these patterns appear, and then measured the diameter of all circles in the pattern and then counted the amount of rings which are present. With my equipment I managed to measure from 1 to 7 rings, where the first one often is immeasurable sometimes because it disappears into the screw at the center of the plate. Now this is what I have, and what I wanted to achieve was to find the speed of the wave in the plate, using the information gathered from the rings. I was told to look into bessel functions and I was referenced to this paper (http://www3.ic.ac.uk/pls/portallive/docs/1/8649699.DOC) which has proven to be quite helpful. Now the actual issue is that I lack the mathematical background, though I have a friend who is willing to help me through this, though the physics part is what is the most troubling. What I really need is someone willing to explain to me how to break it down mathematically. Guide me such that I can properly apply my data, and then sit down with my friend where he can explain the mathematical process to it in terms of solving any potential differential equations.

    I basically want to determine the speed of the wave through the plate by using the circular nodal patterns/standing wave patterns of the salt which are formed on the circular plate. Though I am quite unsure how to interpret the data. My teacher is supposed to help me, though it seems like the topic is a bit beyond him as well, therefore I seek guidance at the PhysicsForums. Any help is greatly appreciated, I find the investigation extremely intriguing though a bit intimidating as well due to its advanced nature, I still hope this is something I will be able to pull off.

    (The attatched file is a photo from the experiment with six circular nodal patterns)
     

    Attached Files:

  2. jcsd
  3. Feb 10, 2015 #2

    Quantum Defect

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    Rossing and Fletcher. http://books.google.com/books?id=SgBF0j2OfKMC&pg=PA73#v=onepage&q&f=false
    Discuss vibrations in circular plates.
    Look at Eqns. 3.11, etc.
    Table 3.2
    Figure 3.8
     
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