For a particular pipe in a pipe-organ, it has been determined that the frequencies 576 Hz and 648 Hz are two adjacent natural frequencies. U

Question

For a particular pipe in a pipe-organ, it has been determined that the frequencies 576 Hz and 648 Hz are two adjacent natural frequencies. Using 343 m/s as the speed of sound in air, determine the following:
(a) Fundamental frequency for this pipe.
(b) Is the pipe is open at both ends or closed at one end?
(c) Length of the pipe.

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Đan Thu 5 months 2021-08-28T11:18:44+00:00 1 Answers 8 views 0

Answers ( )

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    2021-08-28T11:20:26+00:00

    Answer:

    (a). The fundamental frequency for the pipe is 72.0 Hz.

    (b). This pipe is open at both ends.

    (c). The length of the pipe is 2.38 m.

    Explanation:

    Given that,

    Frequency f₁= 576 Hz

    Frequency f₂ = 648 Hz

    Speed of sound = 343 m/s

    We need to calculate the length of the pipe

    Using formula of frequency

    F_{2}-f_{1}=\dfrac{v}{2l}

    Put the value into the formula

    648-576=\dfrac{343}{2l}

    l=\dfrac{343}{2\times72}

    l=2.38\ m

    (a).We need to calculate the fundamental frequency for the pipe

    Using formula of fundamental frequency

    f=\dfrac{v}{2l}

    Put the value into the formula

    f=\dfrac{343}{2\times2.38}

    f=72.0\ Hz

    This pipe is open at both ends.

    Hence, (a). The fundamental frequency for the pipe is 72.0 Hz.

    (b). This pipe is open at both ends.

    (c). The length of the pipe is 2.38 m.

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