You wiggle a string,that is fixed to a wall at the other end, creating a sinusoidalwave with a frequency of 2.00 Hz and an amplitude of 0.07

Question

You wiggle a string,that is fixed to a wall at the other end, creating a sinusoidalwave with a frequency of 2.00 Hz and an amplitude of 0.075 m. Thespeed of the wave is 12.0 m/s. At t=0 the string has a maximum displacementand is instantaneously at rest.Assume no waves bounce back from the far end of the wall. Find the angular frequency, period, wavelength,and wave number. Write a wave function describingthewave. Write equations for the displacement, as a function of time, of the end of the string that is being wiggled and at a point 3.00 m from that end. Determine the speed of the medium and draw history and snapshot graphs for the waves created.

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Bình An 4 years 2021-07-17T08:48:16+00:00 1 Answers 20 views 0

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  1. taiduc
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    2021-07-17T08:49:42+00:00
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    Answer:

    Explanation:

    A general wave function is given by:

    f(x,t)=Acos(kx-\omega t)

    A: amplitude of the wave = 0.075m

    k: wave number

    w: angular frequency

    a) You use the following expressions for the calculation of k, w, T and λ:

    \omega = 2\pi f=2\pi (2.00Hz)=12.56\frac{rad}{s}

    k=\frac{\omega}{v}=\frac{12.56\frac{rad}{s}}{12.0\frac{m}{s}}=1.047\ m^{-1}

    T=\frac{1}{f}=\frac{1}{2.00Hz}=0.5s\\\\\lambda=\frac{2\pi}{k}=\frac{2\pi}{1.047m^{-1}}=6m

    b) Hence, the wave function is:

    f(x,t)=0.075m\ cos((1.047m^{-1})x-(12.56\frac{rad}{s})t)

    c) for x=3m you have:

    f(3,t)=0.075cos(1.047*3-12.56t)

    d) the speed of the medium:

    \frac{df}{dt}=\omega Acos(kx-\omega t)\\\\\frac{df}{dt}=(12.56)(1.047)cos(1.047x-12.56t)

    you can see the velocity of the medium for example for x = 0:

    v=\frac{df}{dt}=13.15cos(12.56t)

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