To recapitulate, the problem with that intuitive view, which
is the whole basis of believing that there is "Doppler
distortion" is that it assumes that the distance from the
driver is the distance from the instantaneous position of
the piston. That's wrong. The distance from the driver,
since it is riding the wave it is creating, is the distance
from its zero or rest position, the position about which it
oscillates. That doesn't change with the nature of the
signal unless there is a DC component.

If the distance from the driver is not changing, there is no
Doppler shift. None of the proposed scenarios which have
the face of the driver oscillating about a rest position
will produce Doppler shift despite intuition.

Sorry, Bob, but I disagree. There is my thought experiment (which I consider
proof). And there is also the claim by an anonymous poster outlining his test
procedure and claiming he measured it.