The problem here is whether the sound source is actually moving relative
to the listener, when the source is a speaker being driven by a complex
waveform. There are models that show that the actual source of the sound is
a point or plane that lies approximately at the center of the motion
described by the cone (I say approximately because the inertia of the cone
and of the air it is acting on may move the source a bit). If these models
are correct, then the source of the sound is not in motion relative to the
listener and therefore Doppler distortion does not and cannot exist in a
speaker. Certainly, this model, exact or not, is more accurate than the
train/whistle model.

The model you describe is a linear approximation of a nonlinear
system. It works because the center is the *average* sound source
position for a signal with no DC component. Once you start thinking
about adding a DC bias, the model breaks down.

As you've agreed, if the sound source is in motion, the system is no
longer linear due to the speed at which sound travels in air, and can
produce doppler distortion (for example, if I were to hold a speaker
in my hands and run back and forth towards and away from you, there
would be doppler, right?).

Ok, so to show that the sound source is moving, we have to show two
things:
1) that the sound source can change position.
2) that the sound source actually does change position while playing a
sound.

for #1, picture an ideal speaker surface. It has perfect frequency
response all the way down to DC. If you put any waveform on its
inputs, it follows it exactly, even if it's just a pure voltage.

So if I put 3 volts on the speaker, say the surface moves forwards 3
feet. If I put -3 volts on the speaker, it moves backwards 6 feed to
an absolute position (relative to its center position) of -3 feet.

Now, while it's at -3 feet bias, I add a small sine wave to the
signal. The voltage vibrates between -3.1 and -2.9 volts, and the
speaker position, relatively to its neutral 0, vibrates around -3.1
and -2.9 feet.

Would you still argue, in this case, that the sound is coming from the
0 foot position? If no, then you will agree that I have demonstrated
that #1 is possible. If yes, then please explain how (make the speaker
excursion 30 miles instead of 3 feet if you like).

Now I will go for #2:

Since I can set the speaker's position however I like by setting the
DC bias, it follows that I can change that position while the high
frequency sound is playing back on top of it. I could move it at say,
1 ft per second -- this speed is far too slow to produce a sound, and
is practically DC. If you agree that I can set the position of the
sound source by adjusting the DC bias, then it follows that I can
*change* the position of the sound source by *changing* the DC bias.
Any change in the position of the sound source is movement of the
sound source (by the definitions of "movement" and "position"), and
any movement of the sound source creates doppler distortion. QED.

Furthermore, if moving the plate at 1ft per second creates doppler
distortion, then moving at, say, 50 hz or whatever would also create
it -- unless you can think of some arbitrary dividing line above which
doppler distortion no longer occurs.


Now, if you fall back on the "but the speaker is linear!" argument
that you haven't let go of yet, then why don't *you* show the source,
experiement, or mathematical derivation that proves that a speaker-air
system is linear? This seems to be an assumption you're holding with
absolutely *no* justification.

Now, as for evidence that shows this occurs, I believe someone in this
thread mentioned an article with measurements of doppler distortion.
Of course, you've already dismissed any possible empirical evidence
ahead of time by saying it's due to some non-linearity in the speaker
itself and not doppler distortion. This shows a grave misunderstanding
of how science works -- we can *never* proove 100% that something
happens. We can only prove that things *don't* happen in certain ways.
If the distortion measured fits the doppler model perfectly (and I'm
pretty sure it does), then we're right to say that by current
scientific knowledge, it's doppler distortion. If you'd like to
hypothesize a new model for that measured distortion, or come up with
an experiment to show that doppler distortion doesn't exist with a
purely linear speaker, then go right ahead.

Ken