- #1
jarvinen
- 13
- 0
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