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Fundamental Frequency of Two Pipe Organs

  1. Sep 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Two organ pipes, open at one end but closed at the other, are each 1.18 m long. One is now lengthened by 2.50 cm


    2. Relevant equations

    λ = nL/4

    fn = nv/4L

    v = λF

    3. The attempt at a solution

    Here's what I tried

    First I tried finding the fundamental frequency when their lengths were equal

    f = (1)(343 m/s)/4(1.18m)
    f = 72.66949153 Hz

    I'm assuming that v = 343 m/s. It does not say that this is the case in the problem.
    Then I tried finding the frequency of the pipe with the extension

    fextended = (1)(343 m/s)/4(1.205m)
    fextended = 71.16182573 Hz

    Having found these two frequencies I then took of the average of them which gave me 71.916 Hz. Unsurprisingly this didn't work. Any suggestions?
     
  2. jcsd
  3. Sep 11, 2012 #2

    rl.bhat

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    Homework Helper

    Pipe need not be resonating in the fundamental mode. So take lambda =(2n +1)L/4 and proceed.
     
  4. Sep 14, 2012 #3
    If you still need help for this problem, try using this equation

    fBeat = fa-fb

    Solve for frequency using f=(nv)/(4L) where fa is the fundamental frequency for the pipe at its original length and fb is the fundamental frequency for the pipe when it is extended.

    And v=344m/s (speed of sound in air)
     
  5. Sep 14, 2012 #4
    Sorry it's been so long since I've replied, its been a busy week.
    But yes you're right

    f_beat = f_a - f_b

    So I found that if I take f_a to be

    f_a = (1)(343 m/s)/4(1.18m)
    f_a = 72.66949153 Hz

    Then the pipe with the increased length

    f_b = (1)(343 m/s)/4(1.205 m)
    f_b = 71.16182573 Hz

    Then
    f_beat = 72.66949153 Hz - 71.16182573 Hz
    f_beat = 1.507 Hz

    Rounded to 3 sig figs, 1.51 Hz is the correct answer.
     
  6. Sep 14, 2012 #5

    rl.bhat

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    Homework Helper

    The problem statement is not complete. What is required in the problem?
     
  7. Sep 14, 2012 #6
    You're right, it is missing a part; I don't know how I managed that. Sorry to waste your time. The missing part is:

    a) Find the frequency of the beat they produce when playing together in their fundamental.
     
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