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## Homework Statement

[/B]Don't know if this goes here or in the advanced bit, thought I'd try here first!

I know the general solution of a 1D wave equation is given by d'Alembert's formula

##u(x,t) = 0.5[u(x+vt,0) + u(x-vt,0)] + \frac{1}{2v} \int_{x-vt}^{x+vt} \frac{\partial u}{\partial t}(x,0) \mathrm dx##.

And I've been given that for my particular wave, ##\frac{\partial u}{\partial t}(x,0)## = 0 for all x, so that's nice because I don't have to worry about the integral in d'Alembert's.

I've also been given that u(x,0) is x+a for -a≤x≤0

and u(x,0) is a-x for 0≤x≤a

and 0 otherwise.

##a## is a real positive constant.

Plot u(x,t) as a function of x at time t=2a/v.

## Homework Equations

## The Attempt at a Solution

My y axis is going to be labelled u(x) and my x-axis is x. I've subbed in t=2a/v into d'Alembert's, and got

##u(x, \frac{2a}{v}) = 0.5[u(x+2a,0) + u(x-2a,0)]##

So u(x+2a) = x+3a for -a≤x≤0

u(x-2a) = x-a for -a≤x≤0

Which means that for -a≤x≤0, my u(x) = 0.5(2x+2a) = x+a

Is that the right sort of thing to do? I'm pretty sure it's not, since it takes me back to where I started.I don't know how to make use of that set of conditions for -a≤x≤0 etc.

I'm really confused about how to plot this.

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