Concentric drivers

All drivers, because they move forward and backwards will have doppler shifts associated with the movement.  The shifts become potentially more of an issue where the driver covers a wide range of frequencies, for example, a wide range driver acting as a woofer which has large low frequency excursions while also carrying high frequencies that are doppler shifted by that movement.  

With a concentric driver, the tweeter in the center is decoupled from the woofer so it itself is not moving because the woofer is moving so there is no particular problems with doppler shift. But, you have raised an interesting issue because the woofer cone may be acting as a waveguide for the tweeter output, and that waveguide is moving in and out thus contributing to a doppler shift.

The bigger issue is the audibility of any such doppler shift.  One would expect it to be greatest with smaller cone fullrange drivers, yet I have never encountered anyone attributing characteristics of the sound of such drivers to doppler shift. This is an interesting issue.
 

In all my 50 years of involvement with audio, I've never heard anyone mention Doppler shift before. I've been using Tannoys for most of those years, I've yet to notice any Doppler shift.

I suggest you may be looking for a problem that doesn't exist.

Regards,

Dan

Doppler (intermodulation) distortion would show up as a reduction in clarity at high SPLs, particularly with bass-heavy, complex music.  

Duke

I cannot recall who was the manufacturer, but I believe it was a builder of large panel speakers who extolled the virtues of law Doppler effect speakers (because of their large radiating surface, panels have quite small excursion, which reduces Doppler effect0. The same would be true of compression drivers and horn loaded drivers.