Because the room needs to be sound-proof, in the simplest sense, this means that the room must also be air-tight. Obviously, an air-tight room is not practical, so ventilation has to be achieved without compromising the sound proofing. There are three principles that must be followed here:

1. Always aim to move a large volume of air slowly, rather than a small volume of air quickly.
2. The inside surfaces of the duct should be non-reflective. This is to damp any internal resonance that may occur in the duct, and eliminates the droning sound that can often be heard in ventilation ducting. The effect of the internal damping within the duct will not however overcome any problems created by violating the first principle.
3. There must not be a direct line of sight from the sound source to the outside world. In other words, you should always move the air around at least one 90° bend.

Here is the one area where I am unhappy with the design I used. The ducting should have been made from MDF board and lined on the inside with an open-celled, non-flammable foam such as glass fibre duct lining or melamine foam.

The problem I have was created by leaving the inner faces of the ventilation duct hard and smooth. This means that when the fan is running at full speed, you can hear a droning note created by a standing wave in the duct. This is really annoying, so I will be replacing the fan duct with one that is lined correctly.

The foam lining inside the duct acts as an absorber, and sufficiently damps the standing wave created by the fan that you cannot hear it anyone. You may still hear air movement if you run the fan too fast, but there will not be that annoying droning pitch caused by a standing wave within the duct.