- #1
jarvinen
- 13
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Infinite string at rest for t<0, has instantaneous transverse blow at t=0 which gives initial velocity of [itex]V \delta ( x - x_{0} )[/itex] for a constant V. Derive the position of string for later time.
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
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