Buzzing after cloth around cone cracked

A few weeks ago I hooked up my Dad's old speaker set to a Sonos Amp. They are Bose 601 Series III stereo speakers. They were working fine until I (it was probably stupid, I know) turned the Bass to max, put the volume at 75% (125W Amp) and played everything that came up when I googled "Songs with the heaviest bass". Well, after 20 minutes or so, one of the speakers started to buzz all of sudden on all the mid frequencies (most of the speakers have cracked cloth but the mid was the first to be noticed). When I looked under the dust cover, the soft material between the edge of the cone and the speaker box/housing was cracked. Whenever I rest my finger on the cone, it stops buzzing. Being that my amp couldn't come close to blowing these speakers on max, I assume it happened because the cloth became brittle with age.

Is there anyway to fix this? Or, more preferably, what is the part called exactly and can I buy it? It doesn't seem like it would be very expensive to replace and these are nice speakers.

Thank you very much for your help