An attenuation device for attenuating sound waves, and a corresponding system and method, generated by a source emitting sound waves having frequencies between f1 and f2 and wherein the pressure levels are between n1 and n2. The attenuation device comprising at least one acoustic absorber comprising at least one non-linear membrane; the attenuation device being configured in such a way that the first face of the absorber is in acoustic communication with the source. The attenuation device also comprises at least one coupling element for coupling the second face with the source, the coupling element being configured to transmit to the second face sound waves according to the sound waves emitted by the source, and of which the phase and/or the amplitude leads to a pressure differential of the sound waves arriving respectively on the first and second face at the same time.