High and mid frequencies aren't the problem. It's the bass waves which tend to bend around things. It's the most annoying thing as far as neighbors are concerned. Building a room inside a room will help immensely but sometimes there's just not the space nor the budget. If you can't afford to build a floating room, you should consider building some bass traps. It's pretty cheap. Cheap even, not just affordable. Just track down some scrap lumber and leftover building materials in the classifieds section of your newspaper.

Basically, build a panel which resonates at bass frequencies, and then add insulation to suck out all that energy, or dampen it. 3M actually has some cool panels which convert sonic energy to sheer, a much more efficient way to do it. They may be spendy.

Remember your vibrating panels have to have good anchor points, just like a stretched guitar string. This ensures that it vibrates instead of flapping in the wind. It should be pretty simple. Some people break it up into different nodes by adding bracing on the back.

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You don't need a weatherman to know which way the wind blows - Robert A. Zimmerman