  What should be the quasinormal modes associated with a spacetime that
contains a naked singularity instead of a black hole? In the present work we
address this problem by studying the scattering of scalar fields on a curved
background described by a Reissner-Nordstr\"om spacetime with $|q| > m$. We
show that there is a qualitative difference between cases with $1 < q^2/m^2
\lesssim 9/8$ and cases with $q^2/m^2 \gtrsim 9/8$. We discuss the necessary
conditions for the well-posedness of the problem, and present results for the
low damped modes in the low $l$ and large $l$ limit. We also consider the
asymptotically highly damped quasinormal modes. We present strong evidence that
such modes are absent in the case of a naked Reissner-Nordstr\"om singularity,
corroborating recent conjectures relating them to classical and quantum
properties of horizons.
