# Homework Help: Phase change from mass in middle of a string

1. Apr 11, 2012

### Koranzite

1. The problem statement, all variables and given/known data

There is a mass M in the middle of an infinite string, of the same linear density on both sides. The reflection coefficient is $r=-ip/(1+ip)$ where $p=ω^2 M/2Tk$
How does the phase change on reflection vary with M, for fixed ω and T?

2. Relevant equations

Phase change = Im(r)/Re(r)

3. The attempt at a solution

I got the expression $\varphi =arctan(1/p)$, which I can't see how it could be right, as it implies that a phase change of $\pi/2$ occurs when the mass is 0. I know that when the mass is 0, there should be no phase change, and it should tend to $\pi$ as the mass tends to infinity (but the arctan function has a maximum value of $\pi/2$). How can I resolve this to get an equation for the phase change that works?