Craig from Calgary, Alberta has built a woodworking shop in the basement of his house. He wants to cut off the sound from there that is travelling up through the heating ducts that run through the room.
First, use aluminium duct tape to seal off all leaks in the ducts. More sound will travel through holes than anything else. While you are at it, caulk shut any plumbing or electrical holes in this area from the basement up towards the house.
Now cover the ducts with several inches of insulation, just like the graphic that shows insulating heating ducts in an uninsulated crawl space. You don't have to worry about vapour barriers because both sides of your insulation will be warm. Regular fibreglass insulation will work well, while special sound proofing bats will work a bit better as they are more dense. Foam insulation will not work at all as they are too rigid and will transmit sound.
You will probably want to cut off the heating system from this room as all the above efforts will be simply useless if sound can just go through the grill and down the duct. Use a separate heating system for the shop, and ideally have a through the wall ventilation system that will help to keep the dust out of the house, and keep all your noise going outdoors rather than upstairs.
Click here for more tips on general sound proofing.