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Wave formula

  1. Sep 24, 2005 #1
    For the traveling wave described by the formula

    y(x,t) = Asin(kx-wt)


    Then the wave is traveling in the +x direction. True or false?

    In the physics textbook I have, it describes a traveling wave by y(x,t) = Acos(kx-wt), using COS instead of SIN. Is there a difference between these 2 formulas? If there is no difference then shouldn't the statement above be true?

    Also

    Would the wave Asin(kx+wt) travel in the opposite direction of Asin(kx-wt)?


    Thank you for your help.
     
    Last edited: Sep 24, 2005
  2. jcsd
  3. Sep 24, 2005 #2

    lightgrav

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    yes, whether you use sin or cos
    is just a "phase offset" of 90 degrees,
    essentially whether you want to watch
    for cos: the peak of the wave
    for sin: its upward-sweeping edge.

    (kx-wt) contrast with (kx+wt)
    for time just bigger than zero, where
    is the argument still zero?
    (x positive) contrast (x negative)
    so the part of the wave you watch goes
    (positive-x) contrast (neg-x) direction.
     
  4. Sep 24, 2005 #3
    Thank you for your reply.

    I would like to make sure if I have understood what you said.

    So (kx-wt) moves in the + x direction and
    (kx+wt) moves in the - x direction

    The question I have says

    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 = 0
    this new wave should have the same displacement as y(x,t) = Asin(kx-wt)

    1 - Acos(kx-wt)
    2 - Acos(kx+wt)
    3 - Asin(kx-wt)
    4 - Asin(kx+wt)

    The correct choice would be 4 - Asin(kx+wt) right? Since it is asking for same displacement and amplitude at time = 0; therefore cannot be choice 2 - Acos(kx+wt).

    Thank you for your help.
     
  5. Sep 24, 2005 #4

    lightgrav

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    right - so if these two waves are on the same medium,
    at t = 0 their displacements add everywhere,
    with (4)+y(x,0) adding to 2Asin(kx)cos(wt) ...

    answer (2)+y(x,0) adds to 2Asin(kx)cos(wt-45)
    that is, their peaks won't line up, to add together,
    until a little bit later time ... wt=45 degrees later.
     
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