To see how two traveling waves of the same frequency create a standing wave. Consider a traveling wave described by the formula:

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.

Required:
Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.

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bonexptip 3 years 2021-07-21T21:41:41+00:00 1 Answers 1 views 0

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  1. Delwyn
    0
    2021-07-21T21:43:14+00:00
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    Answer:

    y_e = 2A sin kx

    y_t = cos wt

    Explanation:

    A standing wave is produced by the reflection of a traveling wave in an obstacle, let’s write the initial traveling wave

            y₁ = A sin (kx -wt)

    let’s write the reflected wave

           y₂ = A sin (kx + wt)

    we find the sum of these two waves

           y = y₁ + y₂

           y = A sin (kx -wt) + A sin (kx + wt)

           

    let’s develop the double angles

           y = A [sin kx cos wt – cos kx sin wt + sin kx cos wt + cos kx sin wt]

           y = A [2 sin kx cox wt]

    we can write this resulting wave

           y_e = 2A sin kx

           y_t = cos wt

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