Sound Power Reduction When Halving Air Flow Velocity and Doubling Grill Area

[Sntpm_83]

If the velocity of air flow through a grill is halved but the area of the grill is doubled, By what factor will the sound power be reduced?
air flow through a grill represents a dipole sound source, so it depends on the 6th power of velocity, but how does it depend on the area? If I take sound power to be directly proportional to the area and v^6, I am getting a reduction in sound power by 15 dB. Is it correct?

 

[sophiecentaur]

I guess that the sound from different parts of the grill will be incoherent so doubling the area should increase the noise by 3dB. That would give an overall improvement of 12dB, I reckon, as long as the air speed over the whole grill is uniform. It may not be as uniform as for a narrower grill unless the taper is nicely gradual or the larger ducting is long.