The "ventilation" issue is probably bogus. A normal undercut of 1/2" (with a threshold if needed) will avoid the door binding against a carpet and might allow enough make-up air for a bathroom exhaust fan to work properly but not for return air from a classroom or any other occupied room. For that kind of space the undercut would have to be at least several inches and that is illegal in most jurisdictions and unsighty. When return air is allowed to pass through a corridor or an adjacent space it must pass through a transfer duct in the wall or ceiling which can be baffled to reduce sound transfer. You should first have a good HVAC contractor or engineer look at the whole system and advise you on how to properly handle the return air from the space. (It can't be working properly now if the undercut is really part of the system) At any rate, the door undercut should be eliminated as part of the HVAC system and then you can add edge seals from Zero. Covering the entire door with a hardwood veneer plywood panel with edge banding helps a lot. Here is a link that might be useful: Zero sound seal gaskets

I can think of no advantage of plaster over drywall except hardness of the finish and there are more important issues involved. The separation wall between the two units must have a fire-resistance rating and that is much easier to obtain with drywall. Here is the code requirement: "R302.3 Two-family dwellings. Dwelling units in two-family dwellings shall be separated from each other by wall and/or floor assemblies having not less than a 1-hour fire-resistance rating when tested in accordance with ASTM E 119 or UL 263. Fire-resistance-rated floor-ceiling and wall assemblies shall extend to and be tight against the exterior wall, and wall assemblies shall extend from the foundation to the underside of the roof sheathing." That means the wall assembly must have been tested by an agency like UL have have a published test number. These tests are expensive so there are few that are for metal lath and plaster. If the studs are wood, in bearing and don't contain plumbing, etc., the UL test number will be U 300 and U 399. The 1 hour rating can be achieved with a layer of 5/8 Type X drywall (U305). For metal lath and plaster, the the lath would need to be 3/8", 3.4 lb per sq. yd. diamond mesh expanded steel and the plaster would need to have a scratch coat of 2 c.f. of vermiculite aggregate to 100 ibs of fibered gypsum and 100 lb. of unfibered gypsum for the brown coat. (U315). The approved manufacturers of the materials used for each of the tested assemblies are listed for each test. there many more tests for drywall than for lath and plaster. It would be far cheaper and easier to construct and get approval for a drywall assembly with no loss of fire protection or sound separation. To improve the sound separation with drywall (I don't how to do it with plaster) add another layer and perhaps hang it on horizontal resilient channels. Seal the perimeter well and avoid back to back electrical outlets or other penetrations. It can help if one side is different from the other. There are many alternate ways to increase sound separation but the 4 principles are: 1. mass - the heavier and thicker the materials the better 2. resiliency - materials that move with the sound reduce it's energy 3. absorbency - materials that are porous slow and trap sound 4. no cracks - cracks and doors defeat the other principles To get the hardness of a plaster finish with the advantages of drywall you can use a veneer plaster system (blue board) if it is available in you market. It's just a thin coat of plaster on a special drywall board and far superior to taped drywall usually at no additional cost. This post was edited by Renovator8 on Thu, Feb 21, 13 at 9:39

Curliegirlie1189 The statement about placing the unit within the structure was not directed at you... I was highlighting a discussion from another thread unrelated to this one. So I realize this was likely not your decision. With that said, that information doesn't hurt you for future reference. I'm not playing around with anything: It's hard to ascertain what someone is doing from a forum board in which a lot of DIY's come to garner information for this or that. I can't count the number of times this occurs. I can only guess based on statistics of others who have come here before you. Conclusions many times are drawn from the topic of the post - the header of the post. You state you are looking to cover up sound related issues, by sound proofing. In other words let's ignore why the sounds are there and just cover them up. Air noise most of the time relates to design of the system. Improper designs will produce more noise. This is most likely due to high static pressure being placed on your system when it runs. Design related problems can be a challenge to over come. I am not there... so with the information you have provided I can only guess. Guessing never leads to anything good. Combustion air is important which is why I posted the warning about it. The last thing you want is a quiet system that kills you in your sleep or makes you really sick.

You're correct that this can be very costly and, unfortunately, you could do this and be disappointed to find it only muffles the sound a bit. One of the reasons is that the tramping and jumping is not only transmitted through the ceiling but through the walls supporting the ceiling. In addition, adding the most effective soundproofing to your ceiling will noticeably lower your ceilings, if that is a concern. I wish I had more helpful advice, but I also hate to see someone spend many thousands of dollars to remedy an issue like this, only to find it is not as great a solution as they had hoped for.