Question about compound woofers

I'm speculating that if higher frequencies are going to be a problem, they'd radiate out into the room (out the back of the outer cone) before reaching this damping material. Using it may still reduce the contribution of the inner driver, and whatever happens in the cavity for cases where they need to be used beyond typical sub frequencies.

Would setting an upper limit to these where possible achieve the goal instead?

(Could be worth a sim to see where the problems are?)
 
I did some homework and believe that you're all right, to some extent, and the outside portion of the cone is most likely the source of anything audible (I was musing that worrying what might be occurring in the space between the two cones reminded me of the paradox of Schrodinger's cat).🙄
Ironically, my concerns have vanished as I have a new focus- the left channel plate amp died (most likely a power supply cap, it's 25 years old). That's a REAL problem for me to tackle.
I guess I'll go with that old saw:
"If it ain't broke, don't fix it".
Thanks again to everyone for all the kind and patient input (especially you, Dave). 🙂
Good listening!
 
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Stuffing some dampening material in between the 2 cones is a bad idea. It will fall apart and rattle at higher spls no matter what you do to contain it firmly. Id consider mechanically coupling the 2 cones together, sort of like KEF did with some of their older speakers, then fill the space with instapak foam just shy of the surrounds.