Re: [Phys-L] How loud is a collapsing building?

[brian whatcott <betwys1@sbcglobal.net>]

David, you asked for order of magnitude style estimates for the sound 
intensity
of  a building collapse.    Here you go:
Taking construction weight at 280 lb/sq ft for a 2-story structure,
ten thousand square feet would weigh 1200 tonnes.
Modeling these numbers as two plates half way up each ten foot story,
we arrive at 600 tonnes at 1.5 meters and 600 tonnes at 4.6 meters above 
ground.

mgh1 = 6E5kg 9.8 N/kg 1.5 m = 8.8 MJ
mgh2 = 6E5 kg 9.8 N/kg 4.6 m = 27 MJ

Supposing the potential energy is equally divided between thermal, 
brittle failure,
ground vibration and airborne vibration we arrive at this energy budget for
airborne vibration of 9 MW

This energy makes noise over a time given by
s = 1/2 a .t^2
          (for S distance(m),  a acceleration (9.8 m/s/s) ,  t time 
(seconds) )
4.6m = 1/2 9.8 m/s/s  t^2 seconds leading to t about  one second.

Supposing the acoustic energy were evenly spread with time, the power 
for one second would be
9 MW at a radius of  50 ft =  15 meters (the building perimeter wall 
from the center)
The surface wave at a distance of 500 meters from the perimeter amounts to
1/ (4 pi 500^2) of the initial surface the spherical wave in free space.
That is 3.2E-7 X 9 MW or 3W /m^2.
There are numerous walls between the source and one's ears however, and 
I will suppose
that each masonry wall provides an absorption of 20% of the incident energy.
In 500 meters distance there might be 50 such walls providing  1 : 
0.8^50 attenuation of
the 3W/m^2 intensity leaving  5E-5 W/m^2 (say 77dB) - rather less loud 
than an elevated train (80dB)
and much quieter than a subway car (100 dB).

Your mileage may (and probably SHOULD) differ

Brian Whatcott

On 6/23/2015 3:07 PM, David Strasburger wrote:
> Setup for a Fermi estimate game that kept me amused last night:
>
> There is a building in my neighborhood that has been declared structurally
> unsound and the adjacent streets have been closed off. Conversation with
> cop at the barrier:
>
> Q: what's up? why is the street closed?
>
> A: that building's about to fall down.
>
> Q: really?
>
> A: yep - any time: could be five seconds, could be a week. But it's coming
> down.
>
> Q: wow, that's going to be something
>
> A: oh you'll hear it all right!
>
>
> After dinner we heard from our house what might have been thunder and
> rushed back into the square, cameras ready, but the building was standing.
> Walking back to the house my son asked me just how loud we would expect the
> sound to be. We worked up an estimate, but I'm quite sure our guess is
> catastrophically wrong because we ended up with 100 dB.
>
> I'm curious how folks on the list would approach the problem. How loud do
> you think the sound would be if and when the building collapses?
>
> Obviously it requires many assumptions, followed by a number of grotesque
> simplifications and a thorough de-subtling. (For instance, my son and I
> supposed that the side walls just evaporated and the second floor and roof
> just fell en masse.)
>
> Here are some basics to work with:
>
> 1) The building has a footprint of roughly 100'x100' and is two stories
> tall. It's a mid-to-early twentieth century masonry commercial building.
>
> 2) We live about 500 m away.
>
>
>
>
>
>
> David Strasburger
> Physics Teacher
> Noble & Greenough School
> (781) 320-7167
>
>
> ________________________
>
> If you really want to go for it, the city's plot plan is here:
>
> http://www.somervillema.gov/sites/default/files/documents/ElmSt240Plans.pdf
>
> The current google satelite pic and streetview of 240 Elm Street Somerville
> MA even shows the bright green wrapping around the scaffolding.
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