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Homework Help: What values of a and b satisfy the following wave equation?

  1. Feb 5, 2009 #1
    1. The problem statement, all variables and given/known data

    For which values of the constants a and b does u(x,t) = sin(ax)sin(bt) satisfy the wave equation Utt = C2uxx?

    2. Relevant equations


    3. The attempt at a solution

    I've taken the partial differentials:
    Ux = acos(ax)sin(bt)
    Uxx = -a2sin(ax)sin(bt)
    Ut = bcos(bt)sin(ax)
    Utt = -b2sin(bt)sin(ax)

    and subbed them into the equation to get:
    -b2sin(bt)sin(ax)+c2a2sin(ax)sin(bt)=0
    so:
    (-b2+c2a2)(sin(bt)sin(ax)) = 0

    But then I'm lost!!

    I have a feeling that I may have gone in completely the wrong direction so any help would be greatly appreciated!!!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 5, 2009 #2

    Gokul43201

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    You have not gone in the wrong direction.

    If p*q=0, what can you say about p and q?
     
  4. Feb 5, 2009 #3
    I know that each of them must equal zero making
    b = ca and a = b/c
    but is rearranging them to make a the subject really all their asking for?! Am i missing something!!?
     
  5. Feb 5, 2009 #4

    Gokul43201

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    Staff Emeritus
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    Gold Member

    This is correct, but you skipped a step, and in the process lost one of the solutions.

    But once have the other solution, that's basically all you are asked to do.
     
  6. Feb 6, 2009 #5
    Thanks Gokul43201, sometimes you just need a nudge in the right direction!!
     
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