Fact: Putting foam in an enclosure or lining a plant room generally makes little difference
Sound from a source within an enclosure or plant room consists of direct and reverberant components. The first of these travels directly, without being reflected from any internal surfaces. Reverberant sound is reflected from one or more surfaces within the enclosure or plant room. An acoustically absorptive lining, such as mineral wool or foam, may reduce the level of reflected sound but it will make no difference to direct sound from the enclosure or plant room.
If the amount of acoustic absorption is doubled, the reverberant sound is halved (reduced by 3dB). Similarly if it is quadrupled, the reverberant sound is correspondingly reduced by 6dB.
In many cases it is not reverberant sound that controls the sound level from an enclosure or plant room, but direct sound, particularly from sources that are relatively close to the area where sound is egressing. When direct sound is the dominant component of sound from the enclosure or plant room, any further reduction to the reverberant sound (by increasing the amount of absorption) makes negligible difference to the overall sound level egressing from the plant room.
In reality the best reduction in the reverberant sound level that can be achieved is around 10dB, equating to an approximate halving in perceived sound level, but that requires the amount of absorption to be increased by a factor of 10. This makes no difference to sound from the enclosure or plant room due to the direct component, which remains constant.