Sound dampening a sliding door?

You're talking about a pocket door, not a sliding door. Yeah, a pocket door slides into the wall cavity but unfortunately short of replacing the door with a solid core door there's not much you can do. The only thing you can do that I can think of is tack up a carpet over the door opening with a slit up the middle to allow you to enter and exit the room. It can't be attached to the door but you CAN attach it to the door frame.

Best of luck with your problem.

'')

The only thing i could think of doing to sound proof it is go to lowes and look for these rolls of rubber stuff that is sticky on one side, its for metal roofs and if you look up dynamat on google you will know what to look for. Its basically the same stuff just cheaper and it is like a sound dampener which would also help keep the sound from coming through so easily. If its possible try taking the door off and pulling off the panel on one side if its not a solid door and roll and stick the stuff inside of it but if its a solid door or you cant get the panel off id just roll the stuff on the inside part of it and then get a thin sheet of wood and tack over top of it to make it look good. Or you could maybe drill a small hole in the top middle and bottom and get the spray foam at lowes called tuff stuff i believe which might help stop sound as well, just spray it through the holes and it expands all inside it.

the problem with a pocket door is the door themselves are usually hollow and thin and even if you do replace the hollow door with a solid door, there is still the fact the when the door is closed there is a empty pocket in the wall(were the door is when its open) that space is not good at stoping sound.
if possible place a tall piece of furniture like a dresser, bookshelf or something up against the wall where the door pockets into, tack a blanket to the door frame and overlap it were the door pockets into the wall, it should help