Sound Attenuation - Main Duct to Branch Ducts

When main ducts are split into branches the sound power level - L_w - 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

dL_N = 10 log(A_b / A_m)                                  (1)

where

dL_N = sound attenuation (dB)

A_b = branch area (m², ft²)

A_m = 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:

dL_{N_branch} = 10 log((20%) / (100%)) 

     = 7 dB

The sound attenuation in the main duct can be calculated:

dL_{N_main_duct} = 10 log((80%) / (100%)) 

     = 1 dB