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Fundamental Frequency of a Membrane

  • 10-05-2010 05:17PM
    #1
    jimjam91
    Closed Accounts Posts: 14 ✭


    Hey guys,

    I've been looking for a formula to calculate the fundamental frequency of a plate under tension but i can't seem to find one that isn't for a string. I want to use the formula to find out the relationship between the tension and the frequency.

    I have an approximate density and fairly accurate measurements of the area of the plate.

    Any help with getting closer to an answer, even if it's very approximate, would be a real help.

    If you need to know anything else about it to help, let me know.

    Thanks in advance:)
    Tagged:


Comments

  • #2
    jimjam91
    Closed Accounts Posts: 14 ✭jimjam91


    I think i may have derived the formula but if anyone knows better, please correct me.

    T=4f²LVρ or T=4f²L²DWρ

    For which:

    T=Tension
    f=Frequency
    L=Legnth (one dmension of the plate)
    V=Volume
    ρ=Density
    W=Width (the other dimension)
    D=Depth

    I used the formula for a string to get this, i'm not sure if that's even the right sort of thing to do.


  • #3
    Reenakjr
    Registered Users, Registered Users 2 Posts: 9 ✭Reenakjr


    Hi,

    Frequency f for a given plate is proportional to the square root of the tension T.
    F = k sqrt(T)

    If F1 and T1 are the new frequency and tension:
    F1 = k sqrt(T1)

    F1 / F = sqrt(T1 / T)
    T1 / T = (F1 / F)^2


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