OK here is some math.

The first pair of sidebands are about -40dBc. Assuming this is caused
by FM for the moment and as stated before, using the standard FM
sideband calculations, this corresponds to a frequency deviation of
about +/- 1 Hz at 4000 Hz. (The 4000 Hz tone is raised and lowered by
1 Hz at a 50 Hz rate.)

Using 344.3 m/sec for the speed of sound and the Doppler equations
found he

http://www.mathpages.com/rr/s2-04/2-04.htm

The relative speed needed to shift 4kHz by 1 HZ is about 0.2 MPH or
0.3 feet/ sec or about 3.5 inches per second.

If I make the simplifying assumption that the loudspeaker cone is
moving back and forth at 50 Hz with a triangular wave rather than
sinusoidal (just to make the math a bit easier). At 50Hz the cycle is
0.02 seconds and the speaker cone would move about 0.07 inches in that
time. Since it is moving back and forth that is +/-0.035 inches. This
seems perfectly reasonable to me.

Working it the other way round, if you assume a loudspeaker is
reproducing a 50 Hz tone, and the cone is moving +/-0.035 inches at 50
Hz, that is about 3.5 inches per second or 0.2 miles per hour. This
speed produces a Doppler shift (frequency deviation) of about 1 Hz to
a 4 kHz tone which corresponds to -40 dBc first sidebands.

So this is an inherent non-linear distortion but it can be reduced by
using a separate woofer and tweeter or making the speaker cone larger
so it does not have to move as far and therefore as fast. But I don't
think it sounds any different than any other form of non-linear
distortion such as intermodulation. But also the magnitude if this
distortion is much larger than produced by any reasonable electronics
it points out that we should stop worrying about the electronics so
much. The electronics are much better than the speakers.

Interesting question, how does the VELOCITY of the cone change as the
50 Hz is increased in frequency at a fixed amplitude. I know from
looking at a speaker that the excursion reduces as the frequency goes
up, but in this case it is the velocity (not the excursion) of the
cone that it key.

Mark