This is not a trick question, but it's a tricky situation. Sounds moving away from you become lower in volume by the inverse square law. So there's a perhaps rhetorical question whether you'd still be able to detect something moving that fast by the time it Doppler-shifted beyond processing. It absolutely works with light. Distant and fast-receding galaxies red-shift out of visible "colors" into infrared. You would need a very loud sound source, moving away very fast, with a starting frequency in the low end of your hearing range in the first place. There are people who can't intake below 30 or 40Hz, which is a whole octave above the typical healthy 20Hz lower limit. So results would vary across the population.