This video begins explaining how insulation has no ability to stop sound in a wall assembly. It does stop high frequency but this is not the main reason for installing insulation in your recording studio or home theater walls.

The insulation is to dampen the wall panels when vibration occurs. Insulation is also a wise choice in your building or room perimeter walls that are in contact with outside elements.

The 2" X 4" framed wall used in the demonstration has R 11 insulation in it. This is typical building procedure for a warm climate as R 11 is 3-1/2" thick so it does not get compressed into the 3-1/2" deep cavity and become useless for the desired purpose, which is not sound proofing.

Basic Tips & Techniques for Soundproofing : How to Insulate a Recording Studio

The video creator goes on to say that getting the thickest insulation you can, like R 38 value type insulation, is best for you.

R 38 insulation is 10 inches thick! You would have to compress this material to less than half of it's original size to get it into the small 3-1/2" framing bay. By doing this you defeat the materials ability to work for heating/cooling purposes, and cramming and compressing it will effectively short circuit the wall assembly.

The insulation will become rigid from so much compaction and allow sound transmission from one side of the wall to the other. This totally defeats your purpose. A 3-1/2" wall gets 3-1/2" inch deep insulation, a 2X6 (5-1/2")wall gets 5-1/2" inch deep insulation.