Amen Slapper. Every single site that deals with sound attenuation or sound control says the same thing--egg crate does nothing to prevent sound from escaping a room, it only decreases reverb (echo or bounce-back of sound waves) inside that room, giving the illusion that it is attenuating sound. If you check dB (sound pressure) from outside the room before and after you install egg-crate there will be no difference because the sound waves go right through the material and into the wall, where it is transmitted by vibration to the other side and reproduced (like a speaker).
The ONLY way to stop this is exactly what 'Slapper said-- seal off the room and do it in a way that vibration cannot travel out by a connection to the framing of the outer wall OR use a deadening agent on the surface of the drywall (usually a heavy material that will not vibrate, like Mass Loaded Vinyl, or MLV) and then apply a hat-channel and a additonal layer of drywall, which will help to attenuate some of the vibration.....
This is the best site I've seen which explains some of the science behind sound proofing in addition to giving you a resource for materials:
SOUNDPROOFING & More Soundproofing!, Super Soundproofing: Practical Noise Control & SoundProofing Solutions /Materials!