1. The problem statement, all variables and given/known data
A tight string lies along the positive x-axis when unperturbed. Its displacement from the x-axis is denoted by $y(x, t)$. It is attached to a boundary at $x = 0$. The condition at the boundary is
$$y+\alpha \frac{\partial y}{\partial x} =0$$ where $\alpha$ is a constant.

Write the displacement as the sum of an incident wave and reflected wave,
$$y(x, t) = e^{−ikx−i\omega t} + re^{ikx−i\omega t},\qquad x > 0,$$ and compute the reflection coefficient, $r$. Writing $r = |r|e^{i\phi}$, show that $|r| = 1$ and find $\phi$.

2. Relevant equations

3. The attempt at a solution
Since the boundary condition applies at $x=0$ and the equation given is only valid for $x>0$ I can’t use that, so what equation should I use?

(If you just apply the condition that the incident and reflected wave are equal at $x=0$, since there is no transmission, you get what I believe is the desired result, but how would one go about this problem with the method it wants)

http://ift.tt/1r9ZXyc