  We consider the propagation of acoustic waves in a 2D waveguide unbounded in
one direction and containing a compact obstacle. The wavenumber is fixed so
that only one mode can propagate. The goal of this work is to propose a method
to cloak the obstacle. More precisely, we add to the geometry thin outer
resonators of width $\varepsilon$ and we explain how to choose their positions
as well as their lengths to get a transmission coefficient approximately equal
to one as if there were no obstacle. In the process we also investigate several
related problems. In particular, we explain how to get zero transmission and
how to design phase shifters. The approach is based on asymptotic analysis in
presence of thin resonators. An essential point is that we work around
resonance lengths of the resonators. This allows us to obtain effects of order
one with geometrical perturbations of width $\varepsilon$. Various numerical
experiments illustrate the theory.
