Wood slats for sound insulation
Using wood for sound proofing sounds like a ton of work compared to the gain you would get from it.  The easiest thing to do (and likely more effective) would be to put in fiberglass batt insulation to fill the dead air space and then double up the sheetrock on both sides (or whichever side is open). Adding mass is the key, preferably at a widely different resonance level from the framing. Sheetrock fits both bills very well.  If you want to do a simple experiment, put your ear on a stud length 2x4 and have somebody tap lightly on the other end and you'll see what I'm talking about.  If you really want to cut down sound transfer, use a wider floor plate and stagger-stud the wall as well.