1. ## Wave Equation

Hey,

Could someone run through a step by step procedure on how to solve a partial differentiation wave equation?

I'm currently trying to figure out this problem:

Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no inital velocity from an initial position u(x,0) = f(x).
Find the displacement u(x,t) for the given initial position f(x).

f(x) = 2x/L 0 <= x <= L/2
2(L-x) / L L/2 < x < L

Thanks

2. Also, what would be the difference if instead the problem stated:

The string is set in motion from its equilibrium position with an inital velocity u(x,0) = f(x)

as opposed to what I wrote above:

The string is set in motion with no initial velocity from an inital position u(x,0) = f(x)

3. Originally Posted by AMIYY4U
Also, what would be the difference if instead the problem stated:

The string is set in motion from its equilibrium position with an inital velocity u(x,0) = f(x)

as opposed to what I wrote above:

The string is set in motion with no initial velocity from an inital position u(x,0) = f(x)
Its equilibrium is $\displaystyle u(x,0)=0$ with initial velocity $\displaystyle u_t(x,0)=f(x)$.

And the other one is the string has no initial velocity so $\displaystyle u_t(x,0)=0$ but its initial displacement is $\displaystyle u(x,0)=f(x)$.