The attenuation of a monochromatic signal in the presence of discrete noise in one dimension is investigated numerically. The predicted Gaussian attenuation is verified by the numerical program, which is based on Riemann's implicit solution of the exact equation for the unidirectional propagation of shockless sound. Two new results are also presented. In the first, the transition from Gaussian to Bessel dependence as a function of resolution in the detection of a signal is observed. This results shows that the fundamental property of time reversibility can only be established if the overall system of the waves and the observer is considered. In the second result, the evolution of the amplitude of a signal injected downstream from the noise is investigated. The Gaussian attenuation is also observed in this case. This result explicitly shows that the attenuation length depends on the distance the signal has traveled, thus displaying memory and breakdown of translational invariance.
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