I've used an aluminum foil-backed tar sheet for sound insulation in cars before as well and in my Jukebox build, but I doubt that'd have much effect on a room.
One thing that I just recently was introduced to, though, that I'd never heard of before is Homasote 440.
It comes in 4x8 sheets 1/2 in thick, It's basically a kind of compressed fire resistant cellulose. It's an insulating panel, but it's also specifically for sound dampening as well.
In my case, i used it to deck the top of a workbench. It's soft, so it won't scratch things you put on the bench, it's a bit "grippy" so you can sand pieces and they generally won't slide around. And it's easy to work with/cheap so once you've torn it up, you just unscrew it from your bench, cut another sheet and screw it back down. I saw the plans using it in Fine Wordworking ages ago, and just now got a chance to build up a bench with it. We'll see how it works.
So, bottom line. I'm not using it like it's intended, but I think it's intended for what you want to do.
It cost me about 25$/4x8 sheet.