You may not believe this but I'm the guy people call to correct these type of problems. In highrise building steel studs and concrete (fire codes) are the the enemy for sound transmission not wood. Air gaps do nothing to slow down sound...they provide a break from one surface or material to another. Frequency and the decibels of the problem sound or sounds is the starting points. A sub woofer from a home theater is way different from voices or a barking Shih Tzu and would be treated differently.