flat cone vs concave cone

Concave cones are currently the most common for speakers such as subwoofers, woofers and midranges, but what would be the advantages of a midrange or woofer with a flat cone?

At least, I think flat cone midranges have better sound distribution and phase response.
As for subwoofers, I think the shape is not important, as due to wavelengths and frequency response, phase issues and sound distribution would be affected by other issues, but now structurally the shape starts to be important, as different shapes contain different ways of distributing the force applied at the center of the cone.
And about the woofers, depending on the diameter, weight of the cone and the frequencies that will be reproduced, questions about the shape of the cone will be more important, as it will be reproducing both the bass, the mid-bass and the mid-range.
 
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If you are comparing "3 D" cones (basically conical with some variations) vs a flat sheet with a voice coil glued to it, 3D structures are way more rigid and easier to vibrate as a whole; while a flat sheet is extremely flexible, bad for a piston trying to push-pull air.

There are flat diaphragm speakers, I know some using a styrofoam sheet, some using a regular cone filled with styrofoam (so front surface is flat), and high Tech ones using a strong but light honeycomb type sheet..
Good and usable if extra care is taken to build them.
 
Don't know about the dispersion side, but the threads on DML systems are good reads

A lot of high-powered SPL comp subs use a cone make of honeycomb and skin that with glass, so there is a conical surface at the back and flat at the front. The coil is in the usual apex of the cone. Exactly the same process to make helicopter blades

Search for "BMR" on Ali, lots of hits for flat midrange and FR drivers
 
FYI/FWWIW, etc., (Fig. 7) Altec's measurements comparing their shallow cone (curvilinear) wide range (mid) bass woofers Vs JBL's deep conical cone variants; notice that except for a few anomalies down low where the big baffle dominates they're basically identical, so imagine it would be near enough the same with a flat disc.
 

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