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Homework Help: Open ended pipe Harmonics Mastering Physics Question

  1. Mar 3, 2008 #1

    TFM

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    [SOLVED] Open ended pipe Harmonics Mastering Physics Question

    1. The problem statement, all variables and given/known data

    Consider a pipe 45.0cm long if the pipe is open at both ends. Use v = 344m/s.
    Now pipe is closed at one end.

    What is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20 Hz to 20000 Hz?

    2. Relevant equations

    [tex] f_n = (2n-1)\frac{v}{4L} [/tex]

    3. The attempt at a solution

    I have an answer that works, but masteringphysics doesn't accept. I first rearranged the equation to give me:

    [tex] (2n-1) = \frac{f_n * 4L}{v} [/tex]

    then:

    [tex] 2n = (\frac{f_n * 4L}{v})+1 [/tex]

    and finally:

    [tex] n = ((\frac{f_n * 4L}{v})+1)/2 [/tex]

    inserting the values gives 52.5 so I inserted 52 as the answer. wrong, I have tried 51-54, all wrong. so I thought tpo go backwards, using:

    [tex] (2n-1) = \frac{f_n * 4L}{v} [/tex]

    and inserting values, to find the value which is the closest to 20000, buit under it - guess what, the value that came out:

    52!

    Any ideas

    TFM
     
  2. jcsd
  3. Mar 3, 2008 #2

    Kurdt

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    The harmonics of a pipe closed at one end are all odd. For n = 2 you have the 3rd harmonic. For n=52 what harmonic do you have?
     
  4. Mar 3, 2008 #3

    TFM

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    It will be the 53rd Harmonic. The trouble is, I have put 53 in, and it says its the wrong answer!
     
  5. Mar 3, 2008 #4

    Kurdt

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    Sorry that third harmonic was a bad example. The harmonics are given by 2n-1. So if n is 52 what is the harmonic. An easier way to have thought about it would to have solved for:

    [tex] f_n = \frac{nv}{4L} [/tex]

    for n = 1, 3, 5,.....
     
  6. Mar 3, 2008 #5

    TFM

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    Using:

    [tex] f_n = \frac{nv}{4L} [/tex]

    and using n = 103,

    I get a frequency of 19684, which is the first odd number below 20000. would this be the harmonic number?

    TFM
     
  7. Mar 3, 2008 #6

    Kurdt

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    Yes n is the harmonic number.
     
  8. Mar 3, 2008 #7

    TFM

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    Success!! n = 103.

    IOne thing does bother me slightly - where does my orginal answer of 52 fit in?

    TFM
     
  9. Mar 3, 2008 #8

    Kurdt

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    2n - 1 is just another way of saying n = 1, 3, 5, .... . So if you stick n = 52 into 2n - 1 you get 103.
     
    Last edited: Mar 3, 2008
  10. Mar 3, 2008 #9

    TFM

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    That makes sense.

    Thanks,

    TFM
     
  11. Mar 3, 2008 #10

    Kurdt

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    What I was originally aiming at was for you to put the n = 52 into that equation and get 103 but I used a stupid example which probably mislead you slightly. :smile:
     
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