An open pipe, 0.29 m long, vibrates in the second overtone with a frequency of 1,227 Hz. In this situation, the fundamental frequency of the

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An open pipe, 0.29 m long, vibrates in the second overtone with a frequency of 1,227 Hz. In this situation, the fundamental frequency of the pipe, in SI units, is closest to:

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Mộc Miên 2 months 2021-07-22T12:30:46+00:00 1 Answers 3 views 0

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    2021-07-22T12:31:48+00:00

    Answer:

    f = 409 Hz

    Explanation:

    We have,

    Length of the open organ pipe, l = 0.29 m

    Frequency of vibration of second overtone, f_2 = 1227 Hz

    It is required to find the fundamental frequency of the pipe. For the open organ pipe, the frequency of second overtone is given by :

    f_2=\dfrac{3v}{2l}

    v is speed of sound

    Let f is the fundamental frequency. It is given by :

    f=\dfrac{v}{2l}

    The relation between f and f₂ can be written as :

    f_2=3f\\\\f=\dfrac{f_2}{3}\\\\f=\dfrac{1227}{3}\\\\f=409\ Hz

    So, the fundamental frequency of the pipe is 409 Hz.              

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