Show ψ(x,t) = f(x-at) + g(x+at) satisfies the wave equation

[MeMoses]

Homework Statement

Show ψ(x,t) = f(x-at) + g(x+at) satisfies the wave equation (a^2)*(∂^2ψ/∂x^2)-(∂^2ψ/∂x^2)=0

Homework Equations

The Attempt at a Solution

I think i just take the derivative twice and end up with something like the second derivative = a^2*second derivative. However how do I actually take the derivative of an equation like this? I know it will involve the chain rule, but how exactly? Thanks for any help.

 

[Haye]

Your f(x-at), set:
y=f(u)
u=x-at

Chain rule: dy/dx=dy/du*du/dx
dy/dx=f'(u)*1

This is how you can differentiate your function, same goes for differentiating to t.
If all goes well, the f'(u) should cancel out.
Also, you have the wrong wave equation there; both differentials are with respect to x. One should be to t.

Hope this helps.