Fundamental Frequency of Two Pipe Organs

  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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    Pipe need not be resonating in the fundamental mode. So take lambda =(2n +1)L/4 and proceed.
     
  4. 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. 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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    The problem statement is not complete. What is required in the problem?
     
  7. 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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