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Mathematical Representation of a Traveling Wave

  1. Dec 1, 2013 #1
    1. The problem statement, all variables and given/known data
    A wave is represented by y = A sin (kx + ωt). Draw two cycles of the wave from x = 0 to x = 2λ at a) t = 0; b) t = T/4, where T = 1/f = 2∏/ω


    2. Relevant equations
    y = A sin (kx+ωt)

    k = 2∏/λ (number of wave peaks)


    3. The attempt at a solution

    I had a really hard time on this problem. From what I could do, for part a, I plugged in t = 0 and from that, I know we would end up with the equation:

    y = A sin (kx)

    From this, I gathered that the wave would be traveling in a -x direction since the sin function is positive. Outside of that though, I had no idea or understanding how to properly draw it...

    Part b, the best I could gather is that in plugging in t = T/4, we'd get an equation of:

    y = A sin (kx +ω(T/4)).

    In taking T = 2∏/ω

    We can find ω and get an equation of:

    ω = 2∏/T

    So our equation will then look like:

    y = A sin (kx + (2∏/T) (T/4))

    In simplifying the equation further, we get:

    y = A sin (kx +∏/2)

    Once again though, I'm lost how to properly draw it. I would really appreciate any guidance on to go about drawing it out. Would this equation also show that the wave is moving in the -x direction?
     
  2. jcsd
  3. Dec 1, 2013 #2
    So I went back to look at this problem again and I think I found what the graph would look like for part a at time zero. I have the document attached. My question for B then, for the equation found for part B, which was:

    y = A sin (kx + ∏/2)

    does this mean then that the graph would still move in the -x direction but shift by half a wavelength to the left?
     

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