A pipe that is open at both ends has a fundamental frequency of 320 Hz when the speed of sound in air is 331 m/s.

Question

A pipe that is open at both ends has a fundamental frequency of 320 Hz when the speed of sound in air is 331 m/s.

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Mộc Miên 4 years 2021-07-22T23:38:44+00:00 1 Answers 261 views 0

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  1. kimcuc
    0
    2021-07-22T23:40:24+00:00
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    Question

    What is the length of the pipe?

    Answer:

    (a) 0.52m

    (b) f2=640 Hz and f3=960 Hz

    (c) 352.9 Hz

    Explanation:

    For an open pipe,  the velocity is given by

    v=\frac {2Lf}{n}

    Making L the subject then

    L=\frac {nV}{2f}

    Where f is the frequency,  L is the length,  n is harmonic number,  v is velocity

    Substituting 1 for n,  320 Hz for f and 331 m/s for v then

    L=\frac {1*331}{2*320}=0.5171875\approx 0.52m

    (b)

    The next two harmonics is given by

    f2=2fi

    f3=3fi

    f2=3*320=640 Hz

    f3=3*320=960 Hz

    Alternatively, f2=2\times \frac {v}{2L} and f3=3\times \frac {v}{2L}

    f2=2\times \frac {331}{2*0.52}=636.5 Hz\\f3=3\times \frac {331}{2*0.52}=954.8 Hz

    (c)

    When v=367 m/s then

    f1= \frac {v}{2L}\\f1= \frac {367}{2*0.52}=352.9 Hz

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