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Organ pipes

  1. Nov 15, 2004 #1
    Hey all, here is the question:
    A friend in another city tells you that she has a pair of organ pipes, one open at both ends, the other open at one end only. In addition, she has determined that the beat frequency caused by the second-lowest frequency of each pipe is equal to the beat frequency caused by the seventh-lowest frequency of each pipe. Her challenge to you is to calculate the length of the organ pipe that is open at both ends, given that the length of the other pipe is 1.10 m. Note that there are two possible answers to this question. List them both, in the order indicated below.
    ?m (shorter)
    ?m (longer)

    I'm not really even sure where to begin. If someone could just point me in the right direction, that would be great

    Thanks
     
  2. jcsd
  3. Nov 15, 2004 #2

    ehild

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    Gold Member

    You have to know that there are standing sound waves in an organ pipes. There is a node at the closed end and an antinode at an open end. So the pipe with both ends open contains an integer number of half-wavelenghts ( its length L = n *lambda/2) and the length of the pipe with one end closed is related to the wavelength as L=(2n+1/2)*lambda/4.

    In addition, you have to know the relation between wavelength (lambda) , frequency (f) and speed of a wave (V). It is lambda=v/f.

    And the beat frequency is the magnitude of the frequency difference.

    ehild
     
    Last edited: Nov 16, 2004
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