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Homework Help: Wave problem

  1. Aug 17, 2008 #1
    Hello everybody.

    I don't know how to find solution and to draw it for this wave problem:
    Uxx+Utt=0
    U(x,0)=0
    Ut(x,0)=1 a )for 0<=x<=1 and
    Ut(x,0)=0 otherwise.
    I have to draw the grafic for t=0, 1, 2 for x element from -5 to 5.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 17, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi Arben! Welcome to PF! :smile:

    Hint: 0 = (DxDx - DtDt)U

    = (Dx + Dt)(Dx - Dt)U.

    = Dx+tDx-tU.

    Does that help? :smile:
     
  4. Aug 18, 2008 #3

    HallsofIvy

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    In other words, since this is a wave equation with c= 1, any solution can be written in the form U(x,t)= f(x+ t)+ g(x- t) so U(x, 0)= f(x)+ g(x)= 0=> f(x)= -g(x).

    Ut(x,t)= f'(x+t)- g'(x-t). Further, since f(x)= -g(x), f'(x)= -g'(x) so Ut(x,0)= f'(x)-g'(x)= 2f'(x). ;Since you are given Ut(x,0) you can integrate to get f.
     
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