When you snap your fingers there are multiple sound waves, but the speed of sound is so fast you can't distinguish individual waves. The frequency of sound waves is around 100Hz to 10kHz so each wave completes one oscillation in 0.01 to 0.0001 seconds.
What you're hearing when you snap your fingers is the envelope i.e. the overall amplitude of the sound waves. When you throw a stone into still water you get an expanding ring of waves moving out, so at the centre it's still then as you move outwards you pass through the waves and beyond them the water is still again. Hearing the finger snap is the same as being struck by the expanding ring of ripples.
