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Waves equation

  1. Nov 13, 2009 #1
    a wave equation is given as A = A cos (kx - ωt)

    so why if someone describes the wave equation to be A = A sin (ωt - kx) , the argument of the sin function changes by a minus sign?

    and is there a meaning to it?

    also i still don't really understand why the minus sign in the first equation signifies wave moving forward whereas a + sign signifies wave moving backwards ...

    thanks a lot for the help!
     
  2. jcsd
  3. Nov 13, 2009 #2
    kx - ωt = kx' - ωt' if both x' > x and t' > t. => The same wave value A cos(kx - ωt) propagates with time in positive x direction.
     
  4. Nov 13, 2009 #3
    You dont have a wave equation there, you have solutions to a wave equation.

    As well, since cos(-z) = cos(z), i.e. cos is an even function you can write the cos solution as A cos (ωt - kx) if you wish.

    The general solution to the wave equation is
    Acos(wt - kx) + Bsin(wt -kx)
    where A and B are determined by the initial or boundary conditions
    If you wrote the general solution in terms of (kx - wt) then the sign of the factor multiplying the sin function would change to accoomdate this.
     
  5. Nov 13, 2009 #4
    oh...

    so cos (kx - ωt) = cos (ωt- kx ) because it is an even function.

    so whats the difference if we choose to write it in sin instead?
     
  6. Nov 13, 2009 #5
    You can write in either way. The initial/boundary conditions will determine the signs and values of coefficients A and B in the general solution Acos(wt - kx) + Bsin(wt -kx).
     
  7. Nov 13, 2009 #6
    oh i see thanks
     
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