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Wave Equation in 1-d Proof/Verify

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Verify that Acos(kx-ωt) and Bsin(kx-ωt) are solutions of the one dimensional wave eqn. if v=ω/k. Does f(x,t)=(ax+bt+c)^2 represent a propagating wave? If yes what is its velocity?


    2. Relevant equations
    I know the partial differ. eqns. for the wave equation are
    d^2 U/dz^2 = 1/c^2 d^2E/dt^2 for the function f(x-ct) + g(x+ct)
    The lapacians for E is μoεo d2E/dt2


    3. The attempt at a solution
    I am just confused as to how to show this? And same for part b.). To verify something would I have to just take any value for v and show it for the first part. (I'll be talking to my prof. about this problem today as well) Thanks any help and hints are appreciated.
     
  2. jcsd
  3. Feb 6, 2012 #2

    BruceW

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    Homework Helper

    I don't really get what you mean here. Usually, the wave equation is just:
    [tex]\frac{\partial^2 U}{\partial z^2} = \frac{1}{c^2} \frac{\partial^2 U}{\partial t^2} [/tex]
    And for the question, they've given you some possible solutions. Its fairly simple to show that they satisfy the wave equation. Think about it - if you just thought you had worked out a solution, then how would you check that it is correct?
     
  4. Feb 6, 2012 #3
    Yeah, I think I was just making the problem harder than it was. I understand it better now I think about it. Thanks!
     
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