# Partial Differentials and wave equation.

1. May 14, 2009

### hhhmortal

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. May 14, 2009

### HallsofIvy

Staff Emeritus
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 $f_{xx}= (1/c^2) f_{tt}$

Last edited: May 15, 2009
3. May 15, 2009

### hhhmortal

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!