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22 February, 21:44

What are the three longest wavelengths for standing sound waves in a 121-cm-long tube that is (a) open at both ends and (b) open at one end, closed at the other?

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  1. 22 February, 23:36
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    Answer:A) For open pipe

    1stπ=484cm

    2nd wavelength=161.3cm

    3rd is=96.8cm

    B) For closed pipe

    1st wavelength=242cm

    2nd=121cm

    3rd wavelength=80.7cm

    Explanation:

    An open pipe produces a standing waves whose wavelength is related to it's length (length of pipe) by nL/4=π, where n represent odd integers 1,2,3 ...

    So the first note called fundamental note or 1st Harmonic is L=π / 4,121=π / 4

    π = 121*4=484cm

    Third harmonic, L=3π / 4

    So π = 4l/3=4*121/3=161.3cm

    The 3rd wavelength is

    Fifth harmonic=

    π = 4l/5=4*121/5=96.8cm

    For a pipe open at one end and closed at the other also called closed pipe

    Fundamental note is

    2L/n = π where n=1,2,3 ... ie integers

    First wavelength

    π=2L=2*121=242cm

    Second wavelength

    π=L=121cm

    Third is

    π=2L/3=2*121/3=80.7cm
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