  When waves impinge on a disordered material they are back-scattered and form
a highly complex interference pattern. Suppressing any such distortions in the
free propagation of a wave is a challenging task with many applications in a
number of different disciplines. In a recent theoretical proposal, it was
pointed out that both perfect transmission through disorder as well as a
complete suppression of any variation in a wave intensity can be achieved by
adding a continuous gain-loss distribution to the disorder. Here we show that
this abstract concept can be implemented in a realistic acoustic system. Our
prototype consists of an acoustic waveguide containing several inclusions that
scatter the incoming wave in a passive configuration and provide the gain or
loss when being actively controlled. Our measurements on this non-Hermitian
acoustic metamaterial demonstrate unambiguously the creation of a
reflectionless scattering wave state that features a unique form of discrete
constant-amplitude pressure waves. In addition to demonstrating that gain-loss
additions can turn localised systems into transparent ones, we expect our
proof-of-principle demonstration to trigger interesting new developments not
only in sound engineering, but also in other related fields such as in
non-Hermitian photonics.
