A forced-air vent easily allows sound waves to travel back and forth between rooms. To control the sound transmission and still allow airflow, you must build baffles around the vents in the room where you wish to control the sound and in any adjacent rooms to which the ducts are connected. While there are many types of insulation available, acoustical fire batts (AFBs) are "suitable for acoustic insulation inside walls, building into panels, or any place where there is a frame or structure to support it," according to ATS Acoustics.
Cut pieces of plywood into 18 inch by 12 inch pieces with a table or circular saw. This will be the front panel of the baffle enclosure.
Cut pieces of plywood as needed to create triangular side and back panels for the baffle enclosure.
Cut pieces of plywood into 1-inch-wide by 6-inch-long strips.
Cut 6-inch-long (minimum) by 1/4-inch-wide slots every 2 inches apart or less through the front panel of the baffle with a saw or router. This will allow air to escape from the baffle enclosure.
Screw in the plywood sides and back to the front panel. Use silicone sealant along the interior edges to ensure the seams will not leak.
Screw in the 1-inch-wide strips to the exterior of the side and back panels so that they are flush with the top edge. These strips will be used to attach the baffle enclosure to the ceiling.
Cut an AFB mineral wool acoustic panel to be 18 inches by 12 inches and then insert it into the baffle so that it covers the slots on the front panel. This will block sound transmission to and from your room while still allowing airflow.
Screw in the baffle enclosure to the ceiling. Apply silicone sealant at the exterior edges where the baffle enclosure meets the ceiling if desired.
Repeat the process for each vent requiring a baffle enclosure.
Construct a secondary baffle within the baffle enclosure for vents requiring additional soundproofing. This can be done by cutting a second baffle front panel from plywood and putting it behind the first acoustic panel, and then placing another acoustic panel behind it prior to mounting it to the ceiling. The shape and interior design of the baffle enclosure can vary greatly depending on your needs and preference. Some manufacturers make advanced and custom baffle units that may be well suited for your needs. Scissors, a utility knife or an electric knife can be used to cut the AFB mineral wool panels to fit inside the baffle enclosure. Glue the acoustic panels inside of the baffle enclosure if desired.
Do not completely block the flow of air from the vent. Always use caution when working with power tools.