  We investigate a time-harmonic wave problem in a waveguide. We work at low
frequency so that only one mode can propagate. It is known that the scattering
matrix exhibits a rapid variation for real frequencies in a vicinity of a
complex resonance located close to the real axis. This is the so-called Fano
resonance phenomenon. And when the geometry presents certain properties of
symmetry, there are two different real frequencies such that we have either
$R=0$ or $T=0$, where $R$ and $T$ denote the reflection and transmission
coefficients. In this work, we prove that without the assumption of symmetry of
the geometry, quite surprisingly, there is always one real frequency for which
we have $T=0$. In this situation, all the energy sent in the waveguide is
backscattered. However in general, we do not have $R=0$ in the process. We
provide numerical results to illustrate our theorems.
