Soundproofing an aquarium pump or filter motor is relatively simple. It pretty much parallels the methods for soundproofing a pool pump or any such motor pump assembly like a boat engine compartment, but just on a much smaller scale. If the aquarium pump is installed within the pedestal or the base of the aquarium and happens to be water cooled, then soundproofing is simply a matter of wrapping the pump completely with America mat. You can glue Velcro to the mat and thus make a sound control blanket for the pump. If the aquarium pump needs ventilation, then the procedure will require placing the pump motor within a sound control enclosure lined once again with the America Mat.
Now many aquarium enthusiasts do not want to wrap their pumps, but would instead like to soundproof the entire enclosure where the pump is positioned, a good idea since most aquarium pedestals are made of wood, and wood transmits sound 1200 times faster than ambient air. This process is also relatively simple. You would line the inside of the aquarium pedestal with the same America Mat, covering all the walls, the bottom and the underneath area where the fish tank sits. And yes, the double doors if applicable. This will definitely quiet an otherwise noisy pump motor. The more mat you use, the better the soundproofing will be, and you will probably not have neurotic fish. The thickness of the mat is also a factor when soundproofing the entire pedestal area. Though I have found that the ½” America Mat works superbly for this application