Soundproofing your jam room could save you from the interruptions of aggravated neighbours and parents by letting you practice without bringing down the house. Soundproofing is a misleading term because it is not possible to completely stop sound from leaving a room. Soundproofing could be more accurately thought of as attempting to isolate sound to one particular room or keeping unwanted noise out. It is not to be confused with acoustic treatment, which is what is done to walls to enhance acoustic properties. Soundproofing can be done in many different ways depending on your situation.
Add fibreglass insulation to your wall if the drywall hasn't yet been put up. On newly built homes, fibreglass insulation absorbs a lot of sound and is vital if you're having a practice room built. This works as insulation against sound, and in the absence of fibreglass you can add foam or paper insulation. If the walls are already up, you can cut a hole between the drywall's studs and insert foam or paper into the hole.
Add another layer of drywall if you are serious about soundproofing. Basically, when sound comes into contact with a wall, only a small portion of the sound energy is able to penetrate the wall's hard surface. This is because of a sudden change in mass, which affects the flow of the sound waves. When you add a layer of drywall, leave a gap of approximately one inch filled with foam or insulation wool to further absorb the sound. If the two walls are completely together, although the increased thickness will improve sound absorption, the fact that they are together means there is only one change in density, and that allows more sound to pass through. Spacing the walls out adds additional changes in density, which dissipates a lot of the sound energy and protects your neighbours.
Apply soundproofing material to the outer layer of your wall if you don't want to put up a new layer of wall or cut into it. You can buy soundproofing mats and a variety of covers that will further insulate the wall. These can be easily affixed according to the specific product's instructions.
Use egg cartons and any foam you can find if you are working on a very small budget. These don't provide much soundproofing, but are better than bare walls. You can also try to seal the room as much as possible to keep sound in. Make sure the door is properly closed, and if you can add a second door, it drastically reduces the amount of sound that escapes. You can also buy special vertical blinds to soundproof windows.
Move your amplifier onto a chair or platform when it is in use. Amps sitting directly on the floor will be a constant source of irritation to any downstairs neighbours. As long as your amplifier is on something else, the sound will be reduced. No matter what efforts you go to, it is difficult to completely soundproof against low-frequency sounds, so there may inevitably be some bass reverberation audible from your practice room.