Room Acoustics

Does anybody know the best and cheapest way to sound proof A bedroom in an apartment to aquire better sound from an audio system,etc.It has to be something I can place on the exterior of the walls...Would really appreciate some recommendations here.Ty...Does carpets and egg cartons work?
Carpet is fine but ditch the egg carton foam. That egg carton is not fire proff and if your looking to make an impression with the ladies forget the foam on the wall. I would look for something suttle such as Michael Green's room tunes for the corners and work around that. I say less with room treatment is best than to much.
Try Cork Wall tiles.
However the objective of room treatment is never to sound proof a room unless its a studio. The priorities are the reflection points and corners. Lots of information available on the net. see on room treatment.
Very little can really be done in an apartment to soundproof a room since most of the trouble comes from the low frequencies that, quite frankly, get right into the structure of the building. Hard to imagine how you could build a second shell inside the room that would be decoupled as much as possible from the building itself. Absorbing materials are all fine, except they will merely soak up the mid and mostly the high frequencies. An array of acoustic panels and sound traps would "tune" the room, but I am afraid would not alleviate the leakage that would elicit complaints from your neighbours. Low level listening is probably a must in your case. A neoprene gasket around the doors would help as you would be surprised how much sound gets out through such openings. If the building is not sound-proofed as it is, you will spend a lot of effort and money and will still, I would think, wind up with complaints from neighbours.
Your only, expensive, solution: Lead Wallpaper! Yes, it does exist. Put on the wall and doors. Doors should be overlapped at the cracks. Unless you build a sound proof chamber, like hearing tests are conducted in, every thing else is second best. But remember, the lead paper might lead to toxic posion.
Sound proofing in an apartment can be done - no problem. I have just finished my "dedicated listening room in an apartment" project. To increase soundproofing you need MASS. Forget carpets and egg cartons. They are useless.
Djw....can you be a little more specific nn what it is you want to accomplish. What is the issue you have with the way the system sounds currently? Slap echo? Issue with neighbors? Issue with spouse? What?

You may need diffusors verses absorbtion.

Share your thoughts and concerns, e.g. as an apartment dweller, I can not mess up the walls, etc. Why only exterior walls? What is the db level you crank it up to for normal listening?

Folks are here to help, but more information would help us.

Tiger, you might be referring to a product called Acoustilead. Not really wall paper but sheet lead that I have used to insulate a shared wall in a condo. I put up the Acoustilead using hot glue and then put a layer of 1/4" sheetrock over it. It worked great and you couldn't see that it was there. Furthermore, being imbedded in the wall, it was not a health hazzard.
Lead Wallpaper? How in the world would I use my X-ray vision to see what the new neighbors look like.

Try binoculars and the bedroom window. Works great for me.