A couple quick tips.
I built three recording studios in the past and there are two critical areas to consider. The first is preventing outside sounds from entering the studio. The same techniques, of course, would prevent sound from inside a home theater from exiting to the rest of the house.
The two most important things are preventing coupling of interior and exterior surfaces and the use of mass to absorb low frequencies.
The idea of the first item is to prevent sound from being transmitted from one surface to another via something common to both surfaces. If you build two walls with offset studs, make sure nothing on the inside wall touches anything on the outside wall.
Also, using different thicknesses of drywall on the opposing sides reduces the chances of getting sympathetic vibrations since the resonant frequencies will be different.
As for the second item, many types of insulation are available and do a good job with mid to high frequencies. But when it comes to deep bass, mass is the only thing that can absorb the energy involved.
Early recording studios used lead sheeting for this purpose. The studio I built used dual cinderblock walls separated by an air space. The blocks were filled with sand as each course went up.
Of course, if there is one floor slab for both rooms, sound can be transmitted through the common floor.
A friend of mine built a sudio in his home. When building the home, he basically poured the floor of the studio separate from the rest of the foundation. He then built a free-standing studio and finally built a house surrounding it. Nothing in the studio was common to the house. It even had its own heating and air conditioning.
Naturally, this is not a practical approach for most home theaters. But if you just keep these two ideas in mind, you will be miles ahead.
None of this, of course, addresses sound treatment within the room itself. That is another topic all together.
- Jim