Resilient channelsSome of you might be thinking of installing a suspended (or "floating") ceiling with resilient channels to reduce sound transmission between upstairs and downstairs floors.
If you go this route and go to the expense and trouble of demolition and remodeling -- or you're building new construction -- make sure that you affix the channels properly to the wood framing. Improper installation can create a "fail" that continues to allow noise transmission between floors.
These illustrations on the UK website "Sound Service" shows a close up of how the resilient channel should be attached to wood floor joists. Attaching them so that they flex away from the wood framing reduces vibration that typically transfers from floor to floor, and this is what's meant by the term "floating."
This PDF from Buildsite offers a spec sheet of how to install a resilient channel, but with no illustrations.
Added in 2023: This YouTube video from Vancouver Carpenter shows you how to do it and explains it well.
The Soundproofing Company site shows an illustration of the different layers involved in a resilient channel wall (not a ceiling). But it shows the cavity being insulated with pink fiberglass, which I don't recommend.
If you've gone this far, you should consider using a professionally dampened soundproofing drywall, such as one from QuietRock or Soundbreak. Using a single layer of "normal" 5/8" gypsum wouldn't be effective.
Don't forget to add sound-dampening materials into the space between the floors (or walls) after you've opened it up, and before you attach the new ceiling. Preferably rockwool batts!
Add more mass, plus some "softer" materials, like sound-absorbing batts (fiberglass or another material, like rock wool). The additional mass can come from affixing an additional layer of drywall or sound board to the backside of the upstairs floor with Green Glue and a few nails, or you can add a layer of mass-loaded vinyl along with the batts, or both. And use flexible, acoustical caulk (like StopGap from Auralex or QuietSeal from PABCO) between the edges of your ceiling and walls when you're finished. You're trying to to reduce both airborne and impact noise between floors, so now is your opportunity to add materials to solve both problems!
** Partially updated in 2023, because some products have new URLs, some businesses have gone away or been absorbed into other companies, and some videos came down and newer ones became available.