Sound attenuation from main ducts to branch ducts.
When main ducts are split into branches the sound power level - Lw - is reduced according the size of the branch, or amount of air to the branch.
The sound attenuation from a main duct to a branched duct can be calculated as
dLN = 10 log (Ab / Am) (1)
dLN = sound attenuation (dB)
Ab = branch area (m2, ft2)
Am = main duct area (m2, ft2)
The attenuation is indicated in the diagram below:
Example - Sound Attenuation from Main Duct to Branched Duct
In an example 20% of the air goes to the branch duct and 80% of the air goes further on in the main duct. The branch duct area is 20% of the main duct area before the branch and the main duct area after the branch is 80% of the main duct area before the branch.
The sound attenuation from the main duct to the branch duct can be calculated:
dLN_branch = 10 log ((20%) / (100%))
= 7 dB
The sound attenuation in the main duct can be calculated:
dLN_main_duct = 10 log ((80%) / (100%))
= 1 dB