The easiest and most cost effective way to soundproof an existing room is to add another layer of soundproofing drywall like Quietrock over the existing drywall - or replace. It's easy and now Lowe's is selling it for $34 per panel. It's very reliable even univeral studios uses it - you have to use materials designed specifically for high stc that won't get short-ciruited and fail when you hang picutres or anything like that on the walls
Edited to add:
Another great alternative is the use of Green Glue damping compound. It comes in a caulk-like container. All you have to do is squirt it over your existing walls, afix a new layer of drywall, seal the seams with acoustical caulk, and refinish the surface! It's easy and inexpensive!
Just to clarify, Soundproofing refers to keeping sound IN or OUT of a room. Sound Conditioning is what you would do to a specialized room like a recording studio or theater. It treats the sound remaining in the room.
To soundproof, you would want to deploy the 4 basic elements of sound isolation. Decoupling, Absorption, Mass and Damping. Consider building a Room within a room.
Take care to address the three most common sources of leaks (flanking):
1 Outlets in the walls, and ceiling can lights.
2 Doors
3 Ventilation.
A common source of mass is standard 5/8" drywall at $7 a sheet.
To soundproof a room you'll want to take each part - the floors, ceilings, and walls - separately.
Start by checking the areas around the windows, doors, and electrical outlets. Are they properly sealed? If not, you'll need to get some acoustical caulk and fill in the cracks.
Are your doors hollow or solid? Try replacing hollow doors with stronger, solid doors to help block sound.
Finally, you'll use a series of techniques to add Green Glue damping compound and extra drywall to the walls and ceilings. This is easier to do if you are working on a building still under construction, but you can soundproof an existing room. All you have to do is apply the Green Glue to your existing surface (as it is), screw the new drywall over top, fill in the seams with acoustical caulk, spackle, and repaint.
Before you know it you'll have a soundproof room!
You will need either an air barrier or massive additional weight to the walls. Auralex makes vinyl sheets that go behind the drywall that create the mass necessary to absorb some of the sound energy. There are also concrete drywall sheets that can be used. Unless you are willing to renovate your room with new drywall and extra heavy doors, you won't be able to 'sound proof' it.
Using simple foam boards can help sound proof a room. You can also change out the carpet.
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"economical" has no comparative or superlative form. You would say "more economical" or "most economical."
Different types of insulation are used for soundproofing. Felt insulation, acoustic foam insulation and mineral fiber are the most common types.
There Are Many Good Soundproofing Insulation Materials, but Insulation and Mass-Load Vinyl Seem to Be the Best. Mass-Loaded Vinyl and Insulation Are Good for Filling Gaps.
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The cheapest and most effective soundproofing system is to use acoustic insulation. These can be made of minerals, felt, foam or various other materials.
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Acoustical (soundproofing) curtain/draperies have a backing of dense vinyl (opaque or clear) to help absorb sound. The fabric panels are coated on the back with this vinyl. Soundproof curtains usually require other accessories (clips, two-sided tape, etc.) to assure their effectiveness. There are stores and websites that specialize in soundproof window coverings. Your best bet is to discuss your needs with a soundproofing specialist to determine what curtains will be the most effective in your home. http://www.acoustic-curtains.com/about.php AND http://soundproofing.org/infopages/curtains.htm You can find some great room darkening and noise reducing scurtains at your local walmart. I would also check out soundproofing.org.