Acoustic doors?

To reduce sound transmission you need one or more air spaces, this reduces the path that sound can travel through.

First option is two or three solid core doors where you create an air gap between each. I don't know your room or construction of your space so I can't elaborate on how and where to hang them.

I had a hollow core door on the utility closet housing our central AC unit. I replaced it with a solid core plus a fiberglass panel on the back and it reduced the sound enormously.

Upgrading the second door to solid core, the hall way door between the utility closet and my listening room removed all noise competing with the music.

Sound works the other way around too. Stopping it from going through to the bedroom is the same approach. Gaskets may be required if you have much space under the door and unless the walls are filled with fiberglass sheets like I've done in my room, the door may no longer be the transmission path after upgrade.

How much do you want to spend and how much sound do you want to stop? An opening as small as 1/4" between the two rooms will cause the sound to get through. Are aesthetics important? Most sound is stopped using gasketing that can be either surface mounted (cheaper) or concealed in the door. Phil Brady.

If Albert constructs his "air spaces" with concrete or lead, great! But the only thing that affects (reduces) sound transmission from one space to another is MASS and STIFFNESS, but primarily MASS, not xtra air spaces. I just love the myth that stuffing a stud wall cavity with fiberglas stops sound transmission, LOL! The only thing doing that will stop, are the screams of the little creatures that choke on the fiberglas ;-)

As for doors, 1-3/4" solid core (MASS) fully gasketed. with a welded steel frame (STIFFNESS) and no less than 1-1/2 pairs of ball bearing hinges (1-1/2 pair actually = 3 hinges ;-)
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Nsgarch I think we are agreeing and disagreeing.

I agree with your comment on mass and that's why I posted the comment about two doors. However, the space between them is some benefit too, especially if a sound panel is attached. (Hals_den said aesthetics were second to performance).

This from Wired Magazine

How Sound Travels

Let's look at sound, and think about how it travels in order to better understand how to stop it or contain it. Sound is made up of energized pressure waves in the air that cause objects in its path (including our eardrums) to vibrate --objects like walls, floors, doors and ceilings. (Deep bass energy is the worst, as you may have noticed when you walk past a dance club or when a car with a booming one-note subwoofer passes by your home.)

Adding loosely packed fiberglass insulation in the wall cavities of interior walls further reduces the energy passing through, in effect making the air between the walls more lossy. Staggering the wall studs (see below) on each side prevents the bass from passing through because it has to move the studs and the wall, which is very hard to do.

This from University of Massachusetts, Amherst, MA.

Sound attenuation batts soak up sound and can improve the STC rating of a wall. We carefully installed 3-1/2 inch thick sound attenuation batts (Owens Corning http://www.owenscorning.com/ 1-800-438-7465) in all stud cavities after the resilient channel was fastened to the wall. We purchased batts that were sized for steel studs. These larger batts extend into and completely fill the hollow profile of the steel studs. Language on the package claims they can improve partition STC ratings by up to 10 decibels.

http://www.owenscorning.com/quietzone/products/products3.asp

Specification from Owens Corning including specification of attenuation with acoustical batting and sealing.

I agree with your comment about solid core 1-3/4 doors. In fact that's what I used in my home and what I suggested in my post.

I also contend two are better than one and better still would be if they did not line up with each other, but rather were staggered. However this is likely not possible in a residence where we have to work with what we have rather than constructing from scratch.