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

[John Denker <jsd@av8n.com>]

Short version:
Empirical evidence suggests that sometimes a collapsing
building is tremendously loud.  Other times not so much.
  https://www.youtube.com/watch?v=jAplTnu2BRI


Longer version:
On 06/23/2015 01:07 PM, David Strasburger wrote:

> Obviously it requires many assumptions, followed by a number of grotesque
> simplifications and a thorough de-subtling.

I agree with the sentiment, but there is a more positive
spin you could put on it:  Try to /bracket/ the answer.
That is, come up with upper and lower bounds.  This is 
one way of obtaining a /controlled/ approximation.  This 
is standard good practice for dealing with ill-posed 
questions.
  https://www.av8n.com/physics/ill-posed.htm

Physics suggests the lower bound is zero.  There are 
lots of scenarios where the building falls down and 
you don't hear anything.
 *) For starters, imagine the walls maintain their
  shape while the top floor comes loose all at once 
  and falls straight down, like a piston in a cylinder.
  It is slowed by a cushion of air ... the world's
  largest whoopie cushion.  This counts as a collapse,
  but might make very little noise
 *) Depending on atmospheric conditions, it may be
  that the sound gets refracted up into the sky,
  essentially a "mirage" geometry, such that the
  observer 500m away is in the acoustical shadow.
  The numbers for this are marginal but plausible, 
  especially on a day with a large lapse rate.
 *) A barrier such as a row of tall buildings or
  a thick woodlot will deflect or absorb the sound.
 *) The building could crumble very gradually.

ON THE OTHER HAND there are lots of scenarios where
the sound could be treeeemendously loud.
 *) The proverbial "slap stick" efficiently converts
  mechanical energy into sound.  Try slapping a ruler
  against a desktop if you don't believe me.
    https://en.wikipedia.org/wiki/Clapper_(musical_instrument)

  I reckon one steel I-beam slapping against another 
  with just the right geometry could make a noise that
  would hurt your ears many hundreds of meters away.
  I'm not saying this will happen, but it could.

 *) Similarly any sort of "pop" phenomenon efficiently
  converts mechanical energy to sound.  Popping a
  balloon or popping a paper bag is an example.

 *) Certain weather conditions (such as a temperature
  inversion) could focus the sound on a zone 500m
  away ... possibly skipping over a row of low
  barriers.

===============================

I don't even know how to quantify the loudness.  Partly this
is my own ignorance, but also there are serious limitations 
in the usual loudness metrics:
  http://www.physics.byu.edu/download/publication/649
By definition, loudness is a subjective perception.  Roughly
speaking, as I understand it:
  a) people are relatively insensitive to white noise;
  b) they are more sensitive to a pure tone; and
  c) they are even more sensitive to a pop or snap sound.

One can think of good evolutionary reasons for this:  Imagine
a saber-tooth cat snaps a twig over there; your ancestors
found it advantageous to notice.

Note that Fourier analysis is misleading;  white noise has
components at all frequencies, and so does a delta function
... but the latter is far more perceptible, for any given
amount of energy.

Sound "intensity" is not useful because it is an /average/
power level.  Depending on how you do the averaging, that 
doesn't make much sense for snap and pop sounds, which are 
very perceptible despite low average power.

There is such a thing as "instantaneous SPL" 
  http://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=2481&context=theses
  http://www.gpo.gov/fdsys/pkg/FR-2009-04-30/html/E9-9645.htm
where 0 dB corresponds to 20 μPa in air or 1 μPa in water.
However, that cannot possibly be meaningful for short pulses;
you could have a narrow delta function with tremendous peak 
SPL but no energy.  Alas, nobody told OSHA that; they have
a recommendation for peak SPL for impulsive noise:
  https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=STANDARDS&p_id=9735
Looking at the energy per pulse seems to make sense, at 
least for short transient pulses.  I haven't been able to
ascertain the reference level or threshold-of-hearing in
energy units.  This is partly my ignorance, but partly
not:  "The processing of impulse sounds ... is also not
well explored."
  http://artsites.ucsc.edu/EMS/music/tech_background/te-03/teces_03.html

The military has an abiding interest in the production, 
propagation, and perception of pop noises.
  http://faculty.plattsburgh.edu/roger.hamernik/CDS_344/PDF_Files/Echos.pdf
It is well known that loud noises can sometimes be heard 
at long distances and sometimes not, often in alternating 
zones of silence and sound.

Also:

a) A sound that starts out as a sharp delta-function SNAP!
at a pointlike source gets converted to a more spread-out
boom and then a rumble as it propagates over distance,
due to dispersion.  A /plane wave/ in air does not exhibit
much dispersion ... but a spherical wave does.  The medium
is the same, but the wave equation in polar coordinates
gives rise to a virtual dispersion term.  Dispersion is
often overlooked and obscured in introductory discussions
of waves.

b) The higher-frequency components are preferentially
absorbed.  The viscosity and the thermal conductivity of 
the air are the controlling parameters here.

Items (a) and (b) make the distant sound less perceptible 
than it otherwise would be.