Can you help me please? The problem is:
1.Solve the wave equation in finite interval with Dirichlet boundary condition at he right and Neumann boundary condition at the left .
2.Choose the initial conditions for right-running waves.
3.Show the phase difference of wave reflection at the boundaries.
I solved the 1'st question by assuming $u_{tt}=c^{2}u_{xx}$
for $0
And the answer is:
$u(x,t)=\sum_{n=0}^{\infty }\left [ A_n \cos \frac{(n+\frac{1}{2})\pi ct}{l}+B_n \sin \frac{(n+\frac{1}{2})\pi ct}{l} \right ]\cos \frac{(n+\frac{1}{2})\pi x}{l} $
But i stuck with part 2. and 3. of the question.
What conditions i should to choose in order to get right-running waves? Thanks for you help!