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Partial Differentials and wave equation.

  • Thread starter hhhmortal
  • Start date
  • #1
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Homework Statement



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



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?
 

Answers and Replies

  • #2
HallsofIvy
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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]
 
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  • #3
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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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