1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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

    User Avatar
    Staff Emeritus
    Science Advisor
    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!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What values of a and b satisfy the following wave equation?
Loading...