This will show you how to do the same with old coffee cups.
Here's what you need, Coffee Cups A LOT of them about 16 per foot of wall.
But these are easily found where ever hot beverages are served. (or the garbage can next to that place). Or ask the owner if you can set up a box for recycling them.
Coffee cups are mostly made from polystyrene and in my opinion is a horrible compound and should be eliminated all together.
The only way to do this is to recycle it until the point that it is no longer possible to produce profit from it.
And a adhesive, you can use just about any kind, spray glue, hot glue, wallpaper adhesive but i find that great stuff spray in foam insulation works the best for this project. You'll need about 8 -10 for a whole room or basement.
Step 1: Step One: Remove Wall or Add a Second One
But works well in empty wall spaces, or as i did for a friend a layer of foam cups and carpet covered plywood did a amazing job, he can now use his basement to practice with his very heavy metal band with out disturbing his neighbors.
Also filled ceiling in basement with cups the sound was reduced at least in half from the basement to the first floor.
P.S Your wall space may be thinner then the height of the cups , so you can just cut them down.