What's the best way to soundproof a room on budget

If you add drywall also consider using Green Glue between the layers. It is not a glue, but rather a sound deadening compound. You can also use mass loaded vinyl.

This website has some good information on various methods and their effectiveness.

Sound Proofing Company

The biggest problem is deep bass. It is almost impossible to stop without major work.

I had Tony Manasian (of Tonian Labs) over at my apt. after I bought a pair of his speakers. His main gig is professional high end installations and consulting and he told me that bass is the hardest to control and advised me to hang some natural fibre mats or rugs behind my speaker to keep sound from transferring down to my neighbors below me.

It worked, to a point, depending on how loud I play my music. The bass is another problem since my speakers roll off around 40Hz. As for the courtyard and when I forget to close the windows, that is another matter.

Good luck,
Nonoise

If you can, stagger the studs in the wall so a stud is only connected to one panel of sheet rock. Then fill the wall with fiberglass insulation, snaking the insulation between the adjoining studs. That keeps the wall from becoming a drum, and damps out higher frequencies. We did this when building the house and it's amazing how well it works. Of course, your room will be two inches smaller :-)

Agreed - if you can do an isolated second wall that is a great solution. That option is discussed on the website I gave above. It is a great solution, although not always the easiest and less expensive.

You should also look at the resilient channel solutions, although they can be somewhat complicated to install.

C'mon guys (Dtc, Electroslacker); the man said he's on a budget. No way he's going to rip out and re-build his wall to install staggered studs for $500 - $600! And using resilient clips and/or channels to 'float' the drywall surface works best in new construction.

Trust me B_limo, adding another layer of sheetrock to the existing wall will get you 90% there without extra hassle/expense -- to say nothing of minimizing the 'noise inconvenience time' to your neighbors while you're doing the work ;~)