Hijacking this thread to ask a related question. Our finished basement doesn’t have insulation between the floors and I want to add it mostly for sound reasons. The basement is/can be a separate apartment so I can see a future of people being down there and not wanting to listen to my elephant-footed children. Is blow-in cellulose or fiberglass the best I’ve got?
Nope!
First you have to understand what kind of sound-transfer you are trying to dampen. If it's elephant-footed children, that's harder to do than if it's just muffling the sound of voices and music and what not.
For dampening the sound of footsteps you need to de-couple the floor upstairs from your basement downstairs. Just as the joists act as a 'thermal bridge' bypassing batts stuffed in-between, the wooden joists also act as an accoustic bridge transferring the stomping of feet or clack of high-heels to the ceiling below.
Solutions range depending on how much time you are willing to spend and how much money. Blown cellulose and/or fiberglass batts will muffle conversations but not do much else in terms fo sound dampening. If you are redoing the upstairs floor for whatever reason it would help to put an underlayment (basically a rubber mat) before laying the floor down on top.
But short of that, you are limited to what you can do from below.
The easiest* (IMO) is to add a second sheet of drywall right under the existing drywall, but to use a de-coupling adhesive like "green glue" between the sheets. This creates a tiny gap that stops most of the accoustic bridging. They cost roughly $5/tube bought in bulk, and you need about one tube per full sheet of drywall.
OR you can use isolation clips/channel on your ceiling and then hang your drywall from that. I find that a bit more finicky and it will further lower your ceiling heigh by another ~1" over the green-glue option.
If you want to go whole-hog, blow cellulose (or use mineral wool if you are feeling $$pendy), then two layers of drywall with either green glue or clips in between. But that's a complete tear-out job, whereas you could just add a second layer of drywall without all the demo and dust. For many basements the ceiling height is already pretty low, so losing an inch or two can be considerable. If you've got "full height" you are in luck.
If you are fortunate enough to have HIGH basement ceilings then I'd do a suspended ceiling with accoustic tiles. It only works when you are willing to loose at least 8" of ceiling height, but it will serve as decoupler, sound absorption and easy-access to utilities which can be important.