I am currently renting a room, that was a living room once, and one side of of walls are just pieces of wood that you can slide on a track. I use the middle one as my "door". But there is a small gap between my door and the other piece, I am thinking if I can fill that space with something then it would reduce the sound from the other side.
I am renting so I don't want to do anything permanent, I was thinking of maybe hanging a thick blanket or something over the gap or just fill the gap between them with something that would not stop the sliding of the door.
Best Answer
There's pretty much nothing you can do so I'll try to save your money from expensive solutions that don't work.
The way to build a soundproofing wall is with a "double skin". You put two sets of studs with an offset, and put drywall on both sides. Each side of the wall has its own set of studs.
When noise (sound waves) in one room hits that side of the wall, it will make it vibrate, but not a lot because drywall is pretty heavy. Then, vibration doesn't go directly through the studs to the other wall because it uses a different set of studs. The inner cavity between both sides is filled with fiberglass to reduce transmission through air. While this is just drywall, it can be pretty good.
So, to stop sound transmission, you need the noise to hit something heavy, like drywall, or better two or three sheets of drywall so it's thicker and heavier, so most of the sound waves get reflected towards the other side instead of making the wall vibrate. Your flimsy "wood" panels do not fit that description, and you can't make them heavier without doing a lot of damage, and there are plenty of holes between them, so... no way.
You may think about buying some soundproofing material for recording studios, and that's when you'll waste your money. The stuff you see on the walls of recording studios like egg-crate shaped foam does no soundproofing (they do that by building double-skin walls as explained above). It is mostly to control sound reflections inside the studio so it doesn't reverberate/echo too much and sound like an empty hallway. If you buy the egg-crate foam, you will have just as much noise, but less money. But you will have less reverberation in your room, I'm not sure you will find it very useful.
Pretty much the only solution that doesn't involve tearing down the flimsy panels and replacing them with a proper wall would be to hang a curtain, made of the thickest heaviest fabric you can find. You can probably convince the landlord to let you install a fixture for that. But it won't be very effective, because even a heavy curtain is a lot lighter than 2-3 sheets of drywall, and it's full of holes.
You treat the slots between the doors with the same kind of stuff we put on doors to make them a bit more airtight and to stop drafts, but that involves glue, and it doesn't really work well for sliding doors...