A system is provided for attenuating tonal acoustic noise associated with a single positive displacement compressor, or multiple positive displacement compressors proximately located from each other. A controller selectably controls the rotational speed and the frequency of operation of each of the compressors. The controller controls the rotational speed of the compressors about a predetermined rotational speed, in a random manner, within the pre-selected speed band to reduce the magnitude of the central tonal acoustic frequency of the pressure pulsations and disperse the sound power over a wider acoustic bandwidth.