When I said +/- 8mm, I meant the range of displacement measureable - with good timing, 0.1 mm accuracy within that range should be achievable.
You can demonstrate the effect very easily with a dual channel oscilloscope.
Trigger one channel off the continuous transmission of a 40kHz transducer, and then look at the phase relationship of the received signal on the other channel as you move either towards or away from the other.
You can do the same, but with longer wavelengths, with an audio signal generator, loudspeaker and microphone.