Standing Waves in Pipes

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Standing Waves in Pipes

There are two types of pipes that you may need to deal with. In each case, you need to be able to work out the wavelength and frequency of the waves.

  1. Pipes with one open end (closed pipe):

    The fundamental frequency standing wave that can fit in a pipe with one open end will be:

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    L = ¼ x wavelength

    So, Wavelength = 4 x L   Frequency = f

    If we increase the frequency and decrease the wavelength, the next wave that will fit will be:

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    L = ¾ x wavelength

    So, Wavelength = 4/3 x L   Frequency = 3 f

    This is the 1st overtone, or the 3rd harmonic.

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    Wavelength = 4/5 x L   Frequency = 5 f

    This is the 2nd overtone, or the 5th harmonic.

  2. Pipes with two open ends:

    The fundamental frequency standing wave that can fit in a pipe with one open end will be:

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    L = ½ x wavelength

    So, Wavelength = 2 x L   Frequency = f

    If we increase the frequency and decrease the wavelength, the next wave that will fit will be:

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    Wavelength = L   Frequency = 2 f

    This is the 1st overtone, or the 2nd harmonic.

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    L =
    3

    2
    x wavelength

    Wavelength = 2/3 x L   Frequency = 3 f

    This is the 2nd overtone, or the 3rd harmonic.

    You may have noticed that you always get an antinode at the open ends and a node at the closed ends. This helps when trying to draw the diagrams!

    In actual fact the waves don't end exactly at the open ends and instead will go slightly further out of the pipe. If you need to adjust for this in a calculation you just add on the extra distance to the length of the pipe.

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