Having built a number of professional sound studios I can confirm that the approach is valid. It won't do a lot for high frequency sound transmission but is very effective for low frequency. Typically 5/8 drywall layers (2-3 depending on the STC requirement) applied with acoustic adhesive with each layer staggered horizontal vs. vertical . This is one product but there are others from which to choose. https://www.amazon.com/Case-Green-Glue-Noiseproofing-Compound/dp/B000SKWD8Y?th=1

Building double walls with sound damping bats in between is also another approach but typically is less effective at low frequency- given less mass. Unless you are trying to emulate studio conditions I'd stick with layering drywall but be advised that at 3 layers you will be adding a lot of weight on the studs and flooring so unless you are building on slab you may want to give consideration to achieving a reasonable balance between STC and weight/as well as cost.

As for high frequency remember that any penetration of a space--for piping, hvac, electric outlets as well as doors and windows is a potential source of kleaking high frequency noise into and out of a space. All penetrations should be sealed with a firestop rated acoustic sealant. Solid core doors and fixed windows--if possible with acoustic caulking and multipanes. Now, none of this addresses sound shaping and the elimination of standing waves etc. but if the purpose is to create a quiet room--and/or shield adjacent structure from noise it will give you a decent result. Good luck.