Organ pipe A, with both ends open, has a fundamental frequency of 360 Hz. The third harmonic of organ pipe B, with one end open, has the sam

Question

Organ pipe A, with both ends open, has a fundamental frequency of 360 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. How long are (a) pipe A and (b) pipe B? (Take the speed of sound to be 343 m/s.)

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MichaelMet 2 weeks 2021-07-21T22:03:11+00:00 1 Answers 1 views 0

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    2021-07-21T22:05:07+00:00

    Answer:

    The length of the pipe A is L_A = 0.4763 m &  the length of the pipe B is L_B = 0.357 m

    Explanation:

    Fundamental  frequency  = 360 Hz

    Velocity = 343 \frac{m}{s}

    (a). Length of the pipe is given by

    L = \frac{V}{2 f}

    Put all the values in above equation we get

    L = \frac{343}{2 (360)}

    L_A = 0.4763 m

    (b). Given that

    The third harmonic of organ pipe B = the second harmonic of pipe A

    \frac{n_B}{4L_B} = \frac{n_A}{2L_A}

    Thus

    L_B = \frac{2 n_{B} L_A }{4n_A}

    Put all the values in above formula we get

    L_B = \frac{2 (3)(0.4763) }{4(2)}

    L_B = 0.357 m

    Therefore the length of the pipe A is L_A = 0.4763 m &  the length of the pipe B is L_B = 0.357 m

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