Ok, me_kaush, lets get some facts straight.
** Hi, i will try my best to reply inline, though for some things like SPL, i'd have to google and try to understand a bit more.
First off, WHERE are these neighbors? Above? Adjacent apartment on the same floor? Are there neighbors on the other side of the existing wall you want to use as one wall of the booth?
** My apartment is on the 4th floor in a 14-floor building. So there are neighbors to my left, right, top and bottom. But the complaining one is on my right side and i've attached a diagram of the top view. The sound gets to him thro' the right side wall that we share as well as thro' my door to his.
What is this "false" ceiling made of?
Please give me an accurate height from existing floor to this false ceiling.
*** Sorry if i gave you this impression, but no, there's no false ceiling already built. I drew it as something i need to do in my section. As of now, the floor-to-ceiling (both concrete) is 8ft.
Have you had neighbors complain already? If so, where is their apartment?
*** Yes, just one, to my right.
Where do you located(country)
*** In New York City, USA
Is there a building inspection department? The reason I ask, is in my country, you are NOT allowed to partition off existing space without obtaining permission by virtue of obtaining a building PERMIT. There are various reasons for this. For one, egress(safety). For another..minimum room size requirements. For another..electrical. For another, HVAC...as should you block off either a supply or return duct from the existing room, the HVAC will not function correctly. Another is to guarantee your construction meets minimum building codes. Another is hardware safety. For instance, should you inadvertantly place a latchset that locks from the outside, someone could get locked in this space. Another is material.. some people will use ANYTHING at thier disposal, to build something that is plain unsafe....like CARDBOARD as shiething ...and don't laugh...I've seen it happen.
*** I'd have to get my condominium board's approval if i need to alter the structure in any way (like knocking down a wall), but if i'm only building something that is not load-bearing, then it is fine. This is to the best of my knowledge, but i will check with my building supervisor. Tks for your note on the HVAC. That thing never occured to me. Btw, in manhattan, i think the only restriction is in how large a room can be, not how small

). Just kidding.
Which brings up the question of PLEXIGLASS. Forget it. It has a lousy Transmission Loss(TL) characteristic, its VERY expensive, and any thickness that would match the TL of the adjacent wall would take your WHOLE budget for one sheet. And THEN, try to cut 1/2" plex...hahahahaha! Have fun. Not only that, you'd need TWO leafs to create an airgap. In fact, personally, I'd forget using plex or glass PERIOD.
*** The only reason i prefer some type of transparent material is because any type of partition that actually blocks light will make my apartment look even smaller

. My idea was to put plexiglass floor-to-ceiling and then add some sound-absorbing material to the inside that i can clip on to the inside during her practice, then remove it once she's done.
Which brings to mind your drawing. This is the problem with sketching things that take DIMENSIONAL space to build. Your simple line drawing doesnt reflect reality. Your drawing suggests LARGE windows on each side of the door. Ha...heres the reality. Even if the wall was 60"(5'), a 32" minimum size door leaves 28". Split it in two for each side and that leaves 14". By the time you add framing for the door(double stud to provide support for a SOLID CORE door, and fraiming for the window, trim etc, you'll be lucky to have a window on each side wider than 8". Hardly worth the trouble. So much for sketchs I see people here all the time with line drawings that may look good, but when it comes time to build,...they scratch their head and go....oh, I forgot that a stud is 1 1/2" thick...oh....and its 3 1/2" wide...crap, now what do I do? I didn't ALLOW for REAL STUFF!!!
*** Yes, sorry, it was just a sketch i drew to illustrate better. I do realise the measurements may need to be more accurate for the actual building part.
Next...since you are ONLY trying to keep sound from transmitting to adjacent neighbors space, and NOT your apartment, I would FORGET a floating floor, and concentrate on THOSE partitions(including ceiling) that seperate you from your neighbor. In this case, that means ONE existing wall and the ceiling...
But without knowing SPECIFIC information(like neighbors location and EXACT existing construction, it would be futile for me to suggest anything positive.
Personally though, from what I DO know, I would build TWO walls as you show. Forget glass. Frame the end wall for a solid core door. Depending on neighbors location, I'd build a covering for the existing window which allows for the application of RESILIANT CHANNEL to be place OVER the window. However, this may NOT be code compliant by virtue of safety concerns. If that were the case, you may NOT be able to cover this window which MAY negate any other solutions by virtue of sound transmission THROUGH this window glass. By virtue of diffraction, Sound may propogate to a neighbors adjacent window, but thats hard to say.
*** I have read about the 2 window setup, but that's generally been to keep outside noise from coming in. Can it also serve the reverse purpose?
The point being, you NEED to decouple 2 layers of drywall on the ENTIRE interior leaf. This means, depending on the nature of the existing dropped ceiling, you MAY need to actually frame another ceiling support from the new walls to the existing wall. Then this will support a new DECOUPLED ceiling leaf by virtue of RESILIANT CHANNEL which will support this new cieling leaf.
However, this is ALL pure conjecture. IF, your wifes vocal db profile reaches high SPL levels, a more robust solution must be utilized. You see, without knowing PRECISE knowlege, we have no way of predicting actuall performance of any solution offered. For instance, if your wifes vocal db profile overcomes the transmission rating of ANY solution offered, whats the point? So, what I suggest is this.
The very FIRST thing I would find out ...is HOW LOUD DO THE NEIGHBORS HEAR HER VOICE???????????? In fact, you need to LISTEN in THEIR apartment. Only you can do this. Secondly, your ears tell you NOTHING. You need to MEASURE the SPL in YOUR apartment as well as THIER apartment. Only then will you be able to tell how much transmission is occuring through the existing partitions, which will THEN tell you what your target TRANSMISSION LOSS RATING should be. Untill then, you are spitting in the wind my friend. You and we can only guess, which means, ANY solution offered is subject to total failure...which means...yup..you got it.....WASTED TIME AND MONEY. So, thats what "I" would do. You need to FIND OUT exactly what is going on and only then design a solution to meet the problem.
*** Unfortunately i don't think i can go to my neighbor's house and try to listen to see how much sound comes through. I've tried talking to him and he's proving to be a complete ass. From googling i find that SPL is sound pressure level, i wonder if there's a software tool i can install on my pc (or mac) to measure it rather than having to buy a tool for this. Do you know?
BTW, I hope these apartments are NOT fed from a common HVAC. IF so, depending on the circumstances, you may NOT be able to successfully build this. On the otherhand, info is king. Which actually brings up another question. Exactly how are you going to VENTILATE this space. Remember, "soundproof" is analogous to "airproof", and if I know singers, they like to breath.
** We have centralised AC/Heater. The radiator is in next to the middle window (3rd). As for ventilation, my wife probably needs to open the window just a bit, and it probably won't matter much that sound gets out that way since all other windows will be closed, so there will be lesser sound coming back in?!
If instead of all this, i can buy a 2-person vocal booth 6ft by 4ft and around 6ft high that has 3 sides with the 4th side being my already existing window, that i can dismantle, that would be perfect. But from the ones i've researched the price is a bit steep for these.
Tks a lot for all your time and advice.
fitZ