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Finding displacement of the string given a function

  1. Jan 31, 2015 #1
    1. The problem statement, all variables and given/known data
    The shape of the wave on the string at t=0 is:
    y=(2x)/(x^2+50)
    The waveform is moving in the +x direction at a propagating speed of 10cm/s. Find the displacement of the string in cm when t=5s and x=30cm

    2. Relevant equations
    ∂^(2)y/∂x^(2)=(1/v^2)*∂^(2)y/∂t^(2)


    3. The attempt at a solution
    I'm completely lost as to how to solve this, I wanted to try and integrate the function to undo the partial derivative but the function they gave was for when t=0 so all the t variables will disappear and I won't be integrating the right function.
     
  2. jcsd
  3. Jan 31, 2015 #2

    Simon Bridge

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    I suspect you are over-thinking things.
    Start by writing down y(x,t). You are given enough information to do that directly.

    (Actually - you start by drawing a sketch of y(x,t=0)... that can help.)
     
  4. Feb 1, 2015 #3
    Okay I managed to get the answer by plugging in x=-20cm into the y=2x/(x^2+50) since the wave is travelling at 10cm/s in 5 seconds x=-20cm will be the spot at 30cm. I never did figure out how to write it down as y(x,t) though, am I supposed to use the general formula y(x,t)=h(x+-vt)?
     
  5. Feb 1, 2015 #4

    mfb

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    Right.
     
  6. Feb 2, 2015 #5

    Simon Bridge

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    That's correct.
    Given y(x, t=0)=f(x) then the same shape travelling in the +x direction with speed v is given by: $$y(x,t)= f ( x-vt)$$ ... a negative speed would, therefore, indicate travel in the -x direction.

    Eg. If ##y( x,0)=A\sin kx##, then $$y ( x, t)=A\sin k ( x-vt) $$

    This is mathematically identical to what you did.
     
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