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Progressive wave equation.

  1. Jun 21, 2013 #1
    1. The problem statement, all variables and given/known data
    A wave moving in the positive Ox-direction has displacement of particle of 0 at the origin, O at time = 0.The displacement-distance graph showed a positive sine graph.
    Write an expression for the variation of the displacement y with time t for the particle at O.


    2. Relevant equations



    3. The attempt at a solution
    My book said that for the particle at O, the equation of motion of particle is y= A sin (ωt).
    But shouldn't it be y= -A sin (ωt -kx) and when x=0, the equation became y=-A sin(ωt) since the particle at O must move down for the wave to propagate to the right hand side.

    And if its y= A sin (ωt - kx), at t=0 and the x=λ/4, then displacement is negative. This is inconsistent with the positive sine graph of displacement-distance graph.

    Someone please lend me a hand on this, Thanks alot.
     
  2. jcsd
  3. Jun 21, 2013 #2

    HallsofIvy

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    Do you not understand that "A" is an arbitrary constant which may be, itself, either poisiitive or negative>?

    I can make no sense at all out of "if it's y= A sin (ωt - kx), at t=0 and the x=λ/4" There was no mention of λ before this. Where did that come from?
     
  4. Jun 21, 2013 #3
    Okay. I will provide more details. The positive sine graph of displacement-distance graph has amplitude of 3 and wavelength of 4 meter while frequency is 2.5 Hz.
    Therefore, the displacement against t for particle at O given by book is y=3 sin (5ωt).

    For your doubt, I assume that when t=0 and the x=λ/4, y= 3 sin (-pi/2) which is negative value. But the positive sine graph of displacement-distance graph at t=0, showed a positive displacement of 3 when its is λ/4 away from O.

    Shouldn't it be y= -3sin wt for particle at O?
     
  5. Jun 21, 2013 #4

    haruspex

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    If 'positive sine graph' means that for small x > 0, y > 0, then I agree: if the sine wave moves towards increasing x then at 0 it must be descending, so y = -|A|sin wt.
     
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