Theoretical sound propagation from a 2D source (wall)

[paolo777]

I have taken equivalent SPL measurements at various distances outside of a building which is housing a noise source. I am trying to prove that sound is leaking from the roof and reaching ground level by diffraction.

If only a single wall was propagating sound how would it decay? Obviously a 3D source should theoretically decay in intensity proportional to 1/r^2 but what of a 2D panel source?

Have not had much luck internet searching or even in text books.

The results do seem to indicate somewhat increasing lower frequency energy the further away from the walls which would indicate the diffraction but i dont think its enough evidence alone.

Any help would be much appreciated,
regards,
Paolo

 

[SylvestreW]

A couple comments
What's the source inside the housing and what's the wall? The reason I ask is why do you believe the wall is vibrating? Unless it's closely coupled with the source, there's no reason to believe the panel is generating the noise. Far more likely is that the noise is being transmitted through the panel (and any gaps on the roof-wall junction)

With respect to your question of a panel source "Engineering Noise Control" by Bies & Hansen has a section on an Incoherent Plane Radiator. It's by no means a simple calculation. It's based on a paper by Hohenwarter in Applied Acoustics #33 (1991).

If you do suspect there's gaps in the junction, then you would presumably get a peak if you do a line measurement at a fixed distance from the wall, along the Z axis, extending from above the roof height to the ground.

-
Aercoustics.com

 

[paolo777]

Its actually a loud band and PA system so SPLs can get quite high on the inside. The building is quite large (sort of a hall) with very high roof (5+ metres) making the measurments u spoke of very difficult and unsafe.

I managed to find the incoherent plane radiator you mentioned in a Hansen book, but am not sure if i can easily relate that to my measurements. I was hoping for some sort of empirical or simplified relationship but there does not appear to be much around.

Thanks a lot for your help.

 

[GregLocock]

The trouble I can see with your method is that the roof probably acts like a 2d panel, so you aren't going to see much difference between the two, to within experimental error.

Assuming that both are actually airtight, then you could measure the vibration on each and estimate the sound radiated by each.

The obvious way of getting what you want is near field intensity - but be warned, it is not by any means a straightforward process at low frequencies, where the wavelength is of the order of the size of the radiator.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[paolo777]

The roof is corrugated tin (quite thin) with sprayed material on the inside to add some sort of mass/diffusion. The walls are what appears to be double brick. As ive mentioned it is just not possible to do an analysis of the roof itself from above the roof as this would be quite unsafe especially as there is no budget to do so.

My assumption is that as you move further away from the hall, all frequencies should decrease if there is a single 2D panel source. However once far enough from the hall wall the low frequencies tend to actually increase for a certain distance range which would seem to indicate diffraction from the roof.

Not sure if this is a legitimate analysis of the data.

 

[GregLocock]

You have a theory, so how can you test it?

How about calculating it for two piston in baffle radiators and see if, ecven in theory, your predcited method would work?



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[paolo777]

Greg,
I'm afraid you have completely lost me at:
"calculating it for two piston in baffle radiators"
would you mind explaining what you mean?
Thanks

 

[GregLocock]

Look up 'piston in semi-infinite baffle" in your aciosutics textbook

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Rob45]

There's another simple point to consider: sound barrier effectiveness is proportional to the surface mass (i.e, pounds per square foot) of the barrier.
If you're comparing cinder block and brick combined, which would have a 1000 Hz transmission loss of 82 dB, to 18 ga. steel with a 1000 Hz transmission loss of 32 dB, guess where the noise is going to come from?
There is a formula relating noise reduction through a wall; this contains a term for the room constant of the receiving room, which, for an exterior wall becomes "very large", leaving the result almost independent of wall area; noise reduction of the wall is dependent entirely on the TL of the wall itself.
NR= TL + 6

Unless this building is quite high, it should be simple to show that most of the noise is coming from the roof, and the practical way of reducing outside noise is to treat the roof, to increase its barrier performance.