Strong bass causing buzzing behind the wall

It sounds like whatever is behind the drywall is "hitting" the drywall as the drywall vibrates or vice-versa or the metal frame attached to the drywall is vibrating against the HVAC ducting. Pushing on the drywall either damps the drywall and/or pushes the two up against each other .. or both. Fortunately HVAC ducting does not care if it is bent :-)

Either use a drilling tool with a depth-stop and/or make one with layers of tape on a drill bit so you can drill the depth of the drywall and not further.  Wrap on the drywall with your knuckles to try to get a feel where the vibration is. Drill a hole in the drywall there (assuming it is not an edge).  Then push something blunt through the hole, an allen-key for example and see if something is right there. If there is, you can probably push something blunt like an allen key through the hole and push whatever is there backwards and then wrap your knuckles to see if it has stopped. If the HVAC is loose and sagging, then you may need to push it up, support it, then blow in some foam from a different hole.  I am with jetter, don't go crazy if you don't know how much space is there.

Yes that will work to stop the vibrating. But you better think about it real good first. Because while this will stop the ducting and drywall from making the noise hitting each other, it will work by bonding them together. What this means is any mechanical sound or vibration in the ducting will be transmitted to the drywall. If its minor you might not notice even up close. But you could just as easily wind up turning the wall into a speaker that lets you hear really good all the furnace air noises and believe me you do not want that! Only you know how loud your furnace is, how close, etc.

But the alternative really good and proper fix is remove the drywall, secure the duct real good, install insulation, and replace, refinish and repaint. That's a lot of see's. Vs one small hole you plug up with some plaster and are done.

If it was me I'd try the hole. That gap filler really expands a lot. Don't drill, use something like a 16 penny nail to poke a hole. That way it will push the duct and not cut through like the drill bit might. Maybe even blunt the nail first. Push the duct back as much as you can, to create some volume to get more bond area. Then just blast it in there. Should work. Fingers crossed!

That Warnes drum by the way, dobro I think its called, yeah pretty powerful and.... repetitive....

Thanks for the quick responses.

The other side of the wall from my listening room is the utility room with the furnace. However, there is a built in book case and a fireplace chimney between the two. From the utility room, I can see what the ducting and drywall wrap look like where it is above/in-front-of the bookcase. However, the part that is buzzing is above the fire place and on the other side of the chimney from the utility room so I can't get to it. 

It looks like the aluminum framing is about 1" high and the ducting sits right above this. I think the ducting is vibrating against the framing, so pushing against the drywall causes the framing to push against the ducting and stops it from vibrating. 

The aluminum framing is pretty flimsy so I am a little concerned that pumping too much of the foam through a small hole might cause the drywall to bulge. But I think this is still probably the easiest fix without pulling everything down (an expensive and messy fix). 

Jetter, the idea that this type of product can bend 2 x4 studs has not been my experience.  Are you speaking from experience, or just going by what you've read on the internet?