I know this is Late, but others may have similar questions:
I am an acoustic consultant. this is my professional specialty. I design this type of arrangement for Hotels Studios and other scenarios where high sound insulation is needed through a wall with a door. Allow for a larger door jamb (door stop) to give space for a larger seal on this surface.
1) the MOST important factor is that the seals on the doors are properly engaged. Next is the quality of the seals on the doors.
I would advise on using rebated strips fitted with double neoprene fin seals on either the door or the frame, around the entire length of the vertical sides and top of the door. a threshold seal is also essential. if you have a smooth threshold a high quality drop seal could work. Cheap drop seals are useless. If you don't need a perfectly flat threshold then a raised rebated threshold with a compression seal would be ideal. I however have a very stron preference for a balloon type compression seal on the vertical and horizontal door jam, and on the frame next to the jamb on the hinge side. (if you put a compression seal on the jamb next to the hinge it gets riped off as the door closes.)
The millimeter accurate fit of the door to the frame is essential. the seals allow for almost no tolerance in distance between the door and the frame. compression seals are slightly more tolerant.
The use of a rebate on the sides, top and bottom of a thick solid door, matched on the frame (like a 2 step stair) will permitt the doubling up of seals in a very efective way. this is only worthwhile on a thick heavy solid or composite door blank.
the wider the gap between the door blanks the better acoustic performance you'll get once the doors are very well sealed. Note when the seal is very good it becomes difficult to close the second door as you are compressing the air in the cavity with no escape route.
You can improve the mid and low frequency performance by placing an acoustic absorber on the back of one door (or both). the acoustically absorbant ceiling tiles used in offices and schools would be an example of a suitable material. this can also be fitted onto the reveals on the frame between the door blanks. Ecophon sell a "Type F" mineral wool tile which is screw-fitted direct to substrate. their "Master" range of tiles are 40mm thick and operate better at lower frequencies. therefore the product is Ecophon Master F.
Alternatively any mineral wool based absorber would be suitable. there are lots of large format ceiling and wall panels at 40mm thick from Ecophon, RockPhon, Custom Audio Designs and others.
New Wall Lining:
Add an extra layer of plasterboard (SoundBloc, FireLine, SoundBloc F, DuraLine or other *heavy* board. SoundBloc F is particularly heavy without costing the price of DuraLine) to the face of the partition you are keeping. This will affect your door frame so do it first.
***Remove*** the plasterboard from the side where you are adding the new wall lining. A wider cavity is far better than a split cavity.
Build a fully independant stud wall. Do not tie back to the old studs.. Timber studs or IWL metal studs. Metal studs can be self supporting from 50mm x 50mm, timber needs at least 63mm so if space is a premium use the IWL system from British Gypsum, Ciniat or Knauf. See the IWL system in the White Book www . british-gypsum.com / white-book-system-selector / systems-overview / linings / gyplyner-iwl (remove the spaces)
keep the new studs at least 10mm away from the old wall studs / bricks.
put at least 50mm mineral wool into each stud frame. I reccomend Rockwool RW45 or Rockwool Flexi or other semi rigid batt. these are acoustically superior and far easier to handle than the APR1200 sold by british gypsum they also dont shed fibres into your hands so you dont get so itchy. they are self supporting and dont fall down to the bottom of the cavity as or after you build the wall.
Apply minimum of 2 layers of SoundBloc or better to the new wall and finish with tape and joint or a 2mm skim
See the details in the white book on using Intumescent sealant at all perimiters during the process to obtain a airtight acoustic seal. especially at the head detail.
If possible cut back the ceiling, build the new studwork up to the soffitt or timbers, and reinstate the ceiling sealing onto the new stud wall.
