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There is so much folklore about soundproofing, but the science and technology is easy to understand. Perhaps because it is expensive and difficult to achieve really good results, people look for 'magic' solutions.
Let's suppose soundproofing had never been invented. OK, let's now invent it - what do we need to do?
We need to prevent sound from passing from one space (the studio for example) to another (the control room). Let's think about the possible ways we could do this...
If you can think of any other possibilities, apply for a Nobel Prize now.
The first option, absorption, sounds good in principle. However, materials that absorb sound are simply insufficiently effective. Light for instance is easily absorbed, so a photographic darkroom doesn't need a door - a folded passageway painted black will work just as effectively. It's a pity that nothing will work as well with sound.
This is perhaps the greatest myth of soundproofing. Absorption alone simply does not work, but it has its place as we shall see in a moment.
Creating an equal and opposite sound wave to cancel the original sound actually does work. The problem is that it only works well for repetitive sounds. For example a noisy piece of machinery can be enclosed, its sound captured, inverted and used to drive loudspeakers. This technique has also been applied to cars and aircraft. Perhaps one day it will be perfected for unpredictable sound sources, but the technology is not ready for the recording studio yet. (A comment below points out that it also works for noise-canceling headphones.)
So, we come to the technique that actually does work - reflecting it back. It is easy to reflect sound - simply set up a solid continuous barrier that possesses significant mass. Mass reflects sound - it's as simple as that. And every time you double the mass of a barrier, the degree of sound insulation improves by 6 decibels.
But what do you do with all that sound that is reflected? Surely that will cause a problem in the studio? Well yes it will, so you absorb it! This is the role of absorption - to dispose of the energy of sound that has been 'proofed' by reflection. This is standard practice in almost every situation where good soundproofing is required.
Oh, what about that last item of collecting sound and channeling it to a disposal zone? Well in theory this is perfectly possible, but it is likely to be over elaborate compared to the normal method. Maybe it just has not been sufficiently explored yet.
One last point - reflecting low frequencies is difficult as mass loses effectiveness by 6 dB for every halving of frequency. However, if the barrier can be made flexible as well as massive, then low frequencies will be absorbed by the barrier bending. It's one of the few instances where absorption actually does produce useful additional insulation.