Finding the solution of the wave equation that satisfies the boundary conditions

[Jack_O]

Homework Statement

Homework Equations

N/A

The Attempt at a Solution

Really stuck with this, i can't work out how to apply the boundary conditions to generate the simultaneous equations to find the specific solution. Can't find any similar examples either.
Help appreciated.

 

[quantumdude]

Do you know D'Alambert's formula? It will give you the solution almost immediately!

 

[Jack_O]

Just looked it up on wikipedia but it confuses me, it doesn't explain it very well.

 

[quantumdude]

You need to translate their notation to yours. They put it thusly.

$$u_{tt}-c^2u_{xx}=0$$

The subscripts indicate partial differentiation, ie $u_{tt}=\frac{\partial^2u}{\partial t^2}$. So their $g(x)$ equals your $e^{-x^2}$ and their $h(x)$ equals your $2cxe^{-x^2}$. It's just plug and chug from there.