Scenario: I'm the owner of a multi-unit 2 story apartment. The people living up and down are cousins to each other and are in the process of switching apartments — long story, don't ask. The upstairs tenants have already moved down but the downstairs tenants have yet to move up, so the top is vacant for a few more weeks.
The lower unit's kitchen has nice vinyl tile that's easy to clean, that the tenants like and are used to, while the upper's kitchen has commercial very low-pile carpet which helps with sound. Kids running around make reducing any low-end sound a priority. The lower unit people have requested similar tile for the upstairs for easy cleaning, but I don't want to get rid of carpet for the aforesaid reason.
The sound on the high end of the scale between units is not a current problem, it's the footsteps/running thuds I would want to keep minimized, which no doubt may be higher with just tile over pine. The rest of the unit will remain carpeted.
There is tongue & groove pine below the carpet. There's very little "give" on the carpet. Can I sandwich the carpet in with quarter-inch subfloor, screwed down well, topped with vinyl? (This is the part where you say yes, ha.)
I may use no-glue tile or tile squares with silicone adhesive. I'm not concerned about absolute perfection in performance/looks for this. If it's not OK to sandwich the carpet, I don't want to put down expensive soundproofing stuff and would tell the tenant to live with carpet.
Seems the only reason not to sandwich would be if a future 300lb'er would jump around cracking the subfloor, but they are all small people.
Best Answer
I think you will regret leaving old carpet on the floor and covering it up. If you are willing to spend $$$ on plywood, why not spend those same $$$ on some foam underlayment for a solid vinyl locking plank floor? The foam is a decent sound deadener, water-proof and resists mold and mildew.
Old carpeting, even a low nap commercial type will hold moisture, breed mold and odors. One bad spill, pet accident, etc will become a smelly problem.
Rip it out and do it right, you won't regret it.