If the AR11 were a ducted-port speaker (I don't think it is), it would
likely be the "port noise complaint" (OUCH!), with air "rushing" or
"whistling" through the port.

It's hard to believe the sound /is/ coming from the speaker when you say "it
isn't related to the music or any movement of the cone or any signal put
through it". Speakers are passive, and do not produce sounds on their own --
other than, perhaps, loud crashing/breaking noises when they're knocked off
a shelf.