"Scott Dorsey" wrote in message

Arny Krueger wrote:

"Bob Cain" wrote in message

I've got an argument that so far has withstood some scrutiny
which shows that Doppler distortion in a myth.

What would refute it and point out any flaw in the reasoning
would be the dynamical expression for the time varying
function of the pressure wave in an infinite tube with an
ideal piston as a function of an arbitrary, time varying
function of the force applied to that piston.

Fool that I am, I'm kinda stuck down here in the real world. Forget
the math, forget the long-winded discussions, the question that
interests me most is whether or not there's Doppler distortion where
it really matters - in the sound field in front of the speaker.

Well, surprisingly enough, Phil actually made the good point that the
woofer position does not directly follow the input signal, but that
the excursion at lower frequencies is exaggerated. This is indeed
the reason that we get Doppler distortion.

I would say that the exaggerated excursion at low frequencies is a
contributing cause for Doppler distortion, but not the only cause.

But, how do we compensate for this? And can we, even?

Of course, reducing the bandwidth to each driver and reducing the
driver excursion as much as possible are crude ways around the problem.

Crude but effective! ;-)

Doppler is exactly proportional to the upper frequency being modulated. Drop
the upper crossover frequency on that woofer by a factor of two, and you
drop the Doppler distortion by 2. Double the diaphragm area, and you get the
same benefit. Subwoofers make even more sense!

BTW, this effect is the justification for the triple-tone tests posted at
http://www.pcavtech.com/techtalk/doppler/ . The FM-related sidebands on the
uppermost tone (4.25 KHz) will be about 4 times larger, compared to the
carrier, as those on the middle tone (1.0 KHz). The two tones are not even
multiples of each other so that the sidebands from each tone will not be
unlikely to land on top the sidebands of the other.

A more exaggerated example of the distortion, though, is found in
coaxial speakers where the moving woofer cone is used as the horn for
the tweeter.

Yes, and I even have a KEF Q-15 to test that with.

However, our preliminary results show that even with a reasonable worst case
(small woofer, relatively high upper frequency) the Doppler tends to get
lost in the AM distortion. Claiming it isn't there is wrong, but getting
worked up about it seems a little foolish.

Here, though, I am not sure the math model is quite so
easy, and it would be interesting to see if anyone can model the
boundary effects near the moving woofer cone.

It's tough enough to work with the case we're working with, which seems to
be far simpler.