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You have to think about more than the walls...
I sound proofed a mother-in-law apartment using Green Glue and 2 layers of 5/8 drywall on each side of a 2x4 batt filled wall. It worked very well.
The Green Glue website has a lot of how-to and detail. Obviously they are selling their product, but they do describe and rank various approaches.
Resilient channel is also very cheap.
The harder part is all the ways sound travels around that wall. You need tightly weatherproofed and draft stopped thick solid core doors (and no pocket doors). Fastening a commercial rubber door draft stop to the bottom of the solid core mdf door, but so that it swept tightly on the floor, probably made the biggest bang for the buck on the in-law apartment. Also, air tight electrical boxes (caulk or with gaskets), copious amounts of acoustic caulk at structural seems, etc.
And then there are the floors and ceilings. Sound travels through rafter bays, attics and floors. If your client is serious about it, you have to address all of it.
I don't know what it does to the STC ratings, but our code lets us build a 2x3 wall when it's interior and non-load bearing. That way you could grab an inch back from whatever you give up to additional drywall thickness.
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