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Open and closed pipe

  1. Dec 12, 2014 #1
    1. The problem statement, all variables and given/known data
    Open and closed pipe, give 5 beats per second.
    Open pipe is 30 cm long and gives a tone of frequency f0.
    Speed of sound is 330 m/s.
    How long do we need to extend closed pipe so both pipes give equal frequencies?

    2. Relevant equations
    Open pipe, fn=n*f1, f1=v/(2L)
    Closed pipe; fn= f*f1, f1 = v/(4L)
    fbeat = f2 - f1
    3. The attempt at a solution
    For open pipe, I assume that f0 is f1, or basic frequency.
    f=v/2L=330 ms-1 / 0,6 m = 550 Hz

    fbeat = f2 - f1
    5 = f2 - 550 Hz
    f2 = 555 Hz.

    Now we need to find the lenght of open pipe.
    4L = v/f2
    l= v/4f2= 0,15 m

    Since i have the lenght of closed pipe, motive is to adjust it so we have frequency of 550 Hz.
    4L = v/f2,
    4*L = 330 ms-1/ 550 Hz
    4*L = 0,6 m
    L = 0,15

    What did I do wrong?
     
  2. jcsd
  3. Dec 12, 2014 #2

    NascentOxygen

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    Staff: Mentor

    I think you mean closed pipe? Better check that calculation, too, using 555Hz.
     
  4. Dec 12, 2014 #3

    ehild

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    Homework Helper
    Gold Member

    You ment closed pipe, didn't you?

    l= v/(4f2)=330/(4*555)=0.1486 m
    You rounded off too early, too much.


    You rounded off too much.
     
  5. Dec 13, 2014 #4
    Yes. lapsus linguae :D

    :(
    I did it again, i got same result like yours.

    Thanks for help guys.
    You are the best :)
     
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