10) Two students want to use a 12-meter long rope to create standing waves. They first measure the speed at which a single wave pulse moves

Question

10) Two students want to use a 12-meter long rope to create standing waves. They first measure the speed at which a single wave pulse moves from one end of the rope to another and find that it is 36 m/s. What frequency must they vibrate the rope at to create the second harmonic

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Mộc Miên 1 year 2021-09-05T14:07:16+00:00 1 Answers 45 views 0

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    2021-09-05T14:08:27+00:00

    Answer:

    To create a second harmonic the rope must vibrate at the frequency of 3 Hz

    Explanation:

    First we find the fundamental frequency of the rope. The fundamental frequency is the frequency of the rope when it vibrates in only 1 loop. Therefore,

    f₁ = v/2L

    where,

    v = speed of wave = 36 m/s

    L = Length of rope = 12 m

    f₁ = fundamental frequency

    Therefore,

    f₁ = (36 m/s)/2(12 m)

    f₁ = 1.5 Hz

    Now the frequency of nth harmonic is given in general, as:

    fn = nf₁

    where,

    fn = frequency of nth harmonic

    n = No. of Harmonic = 2

    f₁ = fundamental frequency = 1.5 Hz

    Therefore,

    f₂ = (2)(1.5 Hz)

    f₂ = 3 Hz

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