To see how two traveling waves of the same frequency create a standing wave. Consider a traveling wave described by the formula y1(x,

Question

To see how two traveling waves of the same frequency create a standing wave. Consider a traveling wave described by the formula
y1(x,t)=Asin(kx−ωt)
This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.
1. Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.
2. At the position x=0, what is the displacement of the string (assuming that the standing wave ys(x,t) is present)?
3. At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.
4. Which one of the following statements about the wave described in the problem introduction is correct?
A. The wave is traveling in the +x direction.
B. The wave is traveling in the −x direction.
C. The wave is oscillating but not traveling.
D. The wave is traveling but not oscillating.
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0this new wave should have the same displacement as y1(x,t), the wave described in the problem introduction.
A. Acos(kx−ωt)
B. Acos(kx+ωt)
C. Asin(kx−ωt)
D. Asin(kx+ωt)

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Ngọc Khuê 5 years 2021-07-14T07:34:40+00:00 1 Answers 88 views 0

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  1. Gerda
    0
    2021-07-14T07:36:07+00:00
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    Answer:

    Check the explanation

    Explanation:

    so basically the standing wave will be created by two waves… y1 and the wave reflected, ie, y2=Asin(wt+Kx)..

    so the resulting wave will be Y= y1 + y2 = 2A Sin(Kx) Cos(wt) = y(x) y(t)

    so y(x)= 2ASin(Kx) and y(t)=Cos(wt)…

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