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Wave equation and displacement

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data
    The displacement of the wave traveling in + x direction is: Y(x, t) = 0.35 (m) Sin (6x- 30t); where x is in meter and t is in second.

    If the wave reaches its maximum displacement after 0.04 sec,
    what is the value of x corresponding to y (max).


    2. Relevant equations
    Y(x,t)=Asin(kx-wt)


    3. The attempt at a solution
    Well I know that with a "standard" sin curve, it reaches a maximum when x=pi/2. However, doesn't this particular displacement equation Y(x, t) = 0.35 (m) Sin (6x- 30t) have a horizontal compression (ie. indicated by what's in the brackets, 6x-30t) so that it's maximum (ie. max displacement) wouldn't occur at 90 degrees on the x axis?

    The answer key says that sin is at a maximum when x=pi/2
    So pi/2 = 6x-30(0.04)
     
  2. jcsd
  3. Jun 16, 2009 #2
    What does multiplying a function by a constant do? Does it change how it behaves?
    Also note that you get vertical compression from the constant 0.35.

    Any sine function reaches its maximum when its argument equals π/2 (You can prove this by differentiating y=A*sin(t)), regardless of any phase shifts brought on by how the argument behaves, and regardless of any compression/stretching brought on by multiplying it by a constant.

    I'm glad you interpreted what the answer key says right. sin(t) is at a maximum when t=π/2, not when x equals π/2, but when the entire argument does.
     
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