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Fundamental Frequency

  1. Jul 24, 2009 #1
    Alright I've been going crazy with this problem. I'm building an electrostatic loudspeaker. In order to get it right I need to find the Fundamental frequency of the vibrating membrane.

    This membrane will be of an elastic substance, Mylar. Approx. 5 microns think with a young's modulus of about 4 GPA.

    How do you go about solving a problem like this?

    I know the solution will have tension, elasticity in the equation. I guess what I'm really asking is what are the group of equations defining modes of vibrations in elastic membranes. I know it will be in the form of a simple harmonic motion

    f= 1/2 PI * SQRT(k/m)


    but there is nothing in that equation relating the restoring force of the membrane due to it's elasticity nor the effects of Air damping it due to drag/viscosity.
     
    Last edited: Jul 24, 2009
  2. jcsd
  3. Jul 24, 2009 #2
    For a circular membrane with fixed rim the frequencies for resonance are given by
    f_nm=j_nm*c/(2PI R)
    where R is the radius of the membrane and j_nm are the zeroes of the Bessel function of first order.
    The lowest value for j_nm in my table is 2.4
    So this will give the lowest frequency.
    You still need the speed of sound in your material (c).
     
  4. Jul 24, 2009 #3
    Oh sorry it would be a rectangle.
     
  5. Jul 24, 2009 #4
    For rectangular, with same fixed rim conditions,
    f_nm=(c/2)*[(n/Lx)^2+(m/Ly)^2]^(1/2)
    (you take square root from the straight bracket)

    Fundamental freq is for n=m=1
    Lx,Ly - dimensions of the membrane
     
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