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vibration membrane exercice physics

  1. Jan 5, 2017 #1
    1. The problem statement, all variables and given/known data

    We have a square membrane and a circular membrane, both fixed from the edges. They are made of the same material with a surface mass σ , and their surface tension is T. We want to tune the lowest eigenfrequency (the fundamental frequency) of both membranes to the same frequency f0
    What would the area of each of the two membranes be in this case?

    Calculate the first five partials of both membranes.

    Comment on the relationship between the partials. •

    Is it possible to tune the membranes harmonically? If so, how could this be achieved?

    2. Relevant equations


    3. The attempt at a solution

    The first question is easy by using equation of eigenfrequency of a circular f = Xm,n/(2*pi*radius)

    where x is the value of the nth non-trivial zero of the mth–order Bessel function, so we equalize this with f0 with X0,1=2.4048 and find the radius

    Same way with eigenfrequency of square with size a: w = c*pi*root(m²/a²+n²/a²) with m=n=1


    But i don't understand what means a "partial" and "tune the membrane harmonically"

    Does anyone have an idea ?

    Best wishes for 2017,
     
  2. jcsd
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