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Organ Pipe Resonance - How long is the pipe?

  1. Jan 25, 2014 #1
    1. The problem statement, all variables and given/known data
    An open organ pipe has a fundamental frequency - corresponding to the first resonant length -of 262 Hz. The room temperature is 20.0°C. What is the length of the pipe. [The answer is 0.66m]

    Given: 262 Hz and 20°C


    2. Relevant equations
    v = 332 + 0.59t
    v = f λ



    3. The attempt at a solution
    v = 332 + 0.59t
    = 332 + 0.59(20°C)
    = 343.8 m/s

    v = f λ
    343.8 m/s = 262 Hz X λ
    λ = 1.3122 m

    Therefore, the length of the pipe is 1.3 m.

    I realize I may be well off. Thanks for your assistance in advance :!!)
     
  2. jcsd
  3. Jan 25, 2014 #2

    tiny-tim

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    Hi MystiqThunder! Welcome to PF! :smile:
    But why would the length be equal to the wavelength? :confused:
     
  4. Jan 25, 2014 #3
    I have no idea... I just figured that is the only way to get a length.
     
  5. Jan 25, 2014 #4

    tiny-tim

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    so the pipe has an open end and a closed end …

    so where are the nodes or antinodes at this frequency?
     
  6. Jan 25, 2014 #5
    Well I am assuming the node is on the closed end and on the open end there is an antinode.
     
  7. Jan 25, 2014 #6

    tiny-tim

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    yes :smile:

    so how long is the wavelength?​
     
  8. Jan 25, 2014 #7
    Oh I see... so the whole pipe would be half a wave length. Right?
     
  9. Jan 25, 2014 #8

    haruspex

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    Not quite. Think of one whole wavelength of a sine wave, but only paying attention to the magnitude at each point. It starts at 0, increases to a maximum, returns to zero, increases to a maximum again, and finally back to zero. What fraction of that does the magnitude of vibration at different distances along the pipe look like?
     
  10. Jan 25, 2014 #9

    tiny-tim

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    one node and one antinode isn't half a wavelength :redface:
     
  11. Jan 25, 2014 #10
    Oh wait! It is a quarter of a wavelength!
     
  12. Jan 25, 2014 #11

    tiny-tim

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    yes!! :smile:

    hmm … sorry … looking at the answer, i think the question must mean the organ pipe is open at both ends​
     
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