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31 July, 15:56

To practice Problem-Solving Strategy 16.1 Standing waves. An air-filled pipe is found to have successive harmonics at 800 HzHz, 1120 HzHz, and 1440 HzHz. It is unknown whether harmonics below 800 HzHz and above 1440 HzHz exist in the pipe. What is the length of the pipe

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  1. 31 July, 16:11
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    Length of the pipe = 53.125 cm

    Explanation:

    given data

    harmonic frequency f1 = 800 Hz

    harmonic frequency f2 = 1120 Hz

    harmonic frequency f3 = 1440 Hz

    solution

    first we get here fundamental frequency that is express as

    2F = f2 - f1 ... 1

    put here value

    2F = 1120 - 800

    F = 160 Hz

    and

    Wavelength is express as

    Wavelength = Speed : Fundamental frequency ... 2

    here speed of waves in air = 340 m/s

    so put here value

    Wavelength = 340 : 160

    Wavelength = 2.125 m

    so

    Length of the pipe will be

    Length of the pipe = 0.25 * wavelength ... 3

    put here value

    Length of the pipe = 0.25 * 2.125

    Length of the pipe = 0.53125 m

    Length of the pipe = 53.125 cm
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