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14 June, 20:06

An air-filled pipe is found to have successive harmonics at 800 {/rm Hz}, 1120 {/rm Hz}, and 1440 {/rm Hz}. It is unknown whether harmonics below 800 {/rm Hz} and above 1440 {/rm Hz} exist in the pipe. What is the length of the pipe?

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  1. 14 June, 20:22
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    The length of the pipe is 53.59 cm

    Explanation:

    Given;

    successive harmonics in the air-filled pipe = 800 Hz, 1120 Hz and 1440 Hz

    For closed pipes, frequency = nv/4L

    where n is odd numbers

    the harmonics are F₀, 3F₀, 5F₀, 7F₀, 9F₀ etc

    the difference between successive harmonic is 2F₀

    2F₀ = 1120 Hz - 800 Hz

    2F₀ = 320

    F₀ = 320 / 2

    F₀ = 160 Hz

    Fundamental frequency (F₀) is given as;

    F₀ = v/4L

    Where;

    v is the velocity of sound = 343 m/s

    L = v/4F₀

    L = 343 / (4 x 160)

    L = 0.5359 m

    L = 53.59 cm

    Therefore, the length of the pipe is 53.59 cm
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