g A rope, under a tension of 233 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the ro

Question

g A rope, under a tension of 233 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by . where at one end of the rope, is in meters, and is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope

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Diễm Kiều 4 years 2021-08-02T16:07:39+00:00 1 Answers 19 views 0

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  1. thienthanh
    0
    2021-08-02T16:08:49+00:00
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    Answer with Explanation:

    We are given that

    Tension=T=233 N

    The displacement of  the rope is given by

    y=(0.320 m)sin(\frac{\pi x}{3})sin(10\pi)t

    a.By comparing with

    y=Asin(kx)sin(\omega t)

    We get

    A=0.32

    k=\frac{\pi}{3}

    \omega=10\pi

    k=\frac{2\pi}{\lambda}

    \frac{\pi}{3}=\frac{2\pi}{\lambda}

    \lambda=3\times 2=6m

    n=2

    n\lambda=2L

    2\times 6=2L

    L=6m

    b.\omega=2\pi f

    2\pi f=10\pi

    f=\frac{10}{2}=5Hz

    Speed,v=f\lambda=5\times 6=30m/s

    c.Let

    Mass of the rope=m

    \mu=\frac{m}{L}=\frac{m}{6}

    v^2=\frac{T}{\mu}

    (30)^2=\frac{233}{\frac{m}{6}}

    900\times \frac{m}{6}=233

    m=\frac{233\times 6}{900}=1.553 kg

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