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I thought that this would be [itex] y_{tt} = c^{2} y_{xx} [/itex] with [itex] y_{t} (x, 0) = V \delta ( x - x_{0} ) [/itex], and [itex] y(x,0) = 0 [/itex]. So use the d'Alembert solution [itex] y = f(x + ct) + g(x - ct) [/itex]. Then applying these gets the forms of f, g.

Is this correct? I am a bit nervous because I am self-teaching some of this wave equation stuff and I am not good at applying the theory to a practical question