With what tension must a rope with length 2.90 m and mass 0.125 kg be stretched for transverse waves of frequency 42.0 Hz to have a waveleng

Question

With what tension must a rope with length 2.90 m and mass 0.125 kg be stretched for transverse waves of frequency 42.0 Hz to have a wavelength of 0.740 m

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Ngọc Diệp 4 years 2021-08-06T00:33:59+00:00 1 Answers 9 views 0

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  1. thnahdat
    0
    2021-08-06T00:34:59+00:00
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    Answer:

    41.64 N

    Explanation:

    Applying,

    v = √(T/m’)……………. Equation 1

    Where v = velocity of the wave, T = Tension of the rope, m’ = mass per unit length of the rope.

    make T the subject of the equation,

    T = v²m’…………….. Equation 2

    But,

    v = λf…………… Equation 3

    Where λ = wavelength, f = frequency

    And

    m’ = m/L……….. Equation 4

    Where m = mass of the rope, L = length of the rope

    Substitute equation 3 and equation 4 into equation 2

    T = (λf)²(m/L)………….. Equation 5

    From the question,

    Given: λ = 0.740 m, f = 42 Hz, m = 0.125 kg, L = 2.9 m

    Substitute these values into equation 5

    T = (42×0.74)²(0.125/2.9)

    T = 41.64 N

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