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The first over tone of an open organ pipe has the same frequency as the first overtone of a closed pipe 3.6 m in length. What is the length of the open organ pipe?

Solution

Given          Length of the closed pipe = L = 3.6 m

Assume        Frequency of the first overtone of the open pipe = f

                         Frequency of the first overtone of the closed pipe = f

Required         Length of the open organ pipe = L =?

Formula

Put the values,

6 Comments

  1. Sana

    This question is solved wrong. The first overtone of a closed organ pipe is the second harmonic, whose frequency is
    f’ = 3v / 4L’
    While the first overtone of an open organ pipe is also its second harmonic, and its frequency is given by
    f” = v / L”
    According to given conditions, the first overtones of both the pipes are equal, so
    f’ = f”
    3v / 4L’ = v / L”
    Which, upon simplification, leads to
    L” = 4L’ / 3
    And by putting values, the length of the open organ pipe is 4.8 m.
    (Kindly make corrections so as others won’t be confused.)

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