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Homework Help: Closed Air Column Problem

  1. Jun 19, 2009 #1
    1. The problem statement, all variables and given/known data

    A closed air column is 60.0cm long. Calculate the frequency of the forks that will cause resonance at:

    a) the first resonant length
    b) the second resonant length

    Note that the speed of sound is 344m/s.

    2. Relevant equations

    Ln = (2n - 1) * [tex]\lambda[/tex] / 4

    fn = (2n - 1)f1, where f1 = V/4L and 4L = [tex]\lambda[/tex]

    3. The attempt at a solution

    I cannot figure out what the actual magnitude of the resonant length is, and don't know how to begin solving the problem.

  2. jcsd
  3. Jun 19, 2009 #2


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  4. Jun 20, 2009 #3
    On the back of the page, the question additionally asks for the third resonant length.

    The textbook provides answers for a, b, and c as 143Hz, 430Hz, and 770Hz respectively. When I reversed the calculations for c), they used a third resonant length of 60.0cm, which was the length of the whole air column.

    I still can't figure out how they got the answers for a and b though :S.
  5. Jun 20, 2009 #4


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    Perhaps I misled with my typo, though you wrote it correctly

    But to state your equations again:
    f1 = v/(4L)
    fn = (2n - 1)*f1

    4*L = 4*.6 = 2.4

    f1 = 343/2.4 = 143

    f2 = 3*f1

    f3 = 5*f1
  6. Jun 21, 2009 #5
    Makes sense, I understand now.

    Thanks again :).
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