When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions of a wave’s free propagation 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’s intensity can be achieved by adding a continuous gain–loss distribution to the disorder. Here we propose a practical discretized version of this abstract concept and implement it 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 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 localized 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.