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Partial Differentials and wave equation.

  1. May 14, 2009 #1
    1. The problem statement, all variables and given/known data

    How can I find out if a function is a solution of a wave equation such as:

    (a) xt
    (b) log(xt)
    (c) x² + c²t²



    3. The attempt at a solution

    Is it simply differentiating the funtion with respect to 'x' twice and equating this to the product of 1/c² and differentiating the function twice with respect to 't'?

    I tried doing it for part (c) and I got 1=1 which means its allowed I guess. As for part (a) I got 0=0 which i suppose it isn't?
     
  2. jcsd
  3. May 14, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, just plug each function into the wave equation and see if they satisfy it: for each function, f, find fxx and ftt and see if they satisfy [itex]f_{xx}= (1/c^2) f_{tt}[/itex]
     
    Last edited: May 15, 2009
  4. May 15, 2009 #3
    Ok, thanks, most of the time they seem to be 1=1 or 0=0 hence satisfying and not satisfying the wave equation i suppose..thanks again!
     
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