  We prove a uniqueness result for Nevanlinna functions. and this result is
then used to give an elementary proof of the uniqueness in the inverse
scattering problem for the equation $ u" + \frac{k^2}{c^2}u=0 $ on $\mathbb R$.
Here $c$ is a real positive measurable function that is bounded from below by a
positive constant, and is close to $1$ at $\pm \infty$.
