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It seems to me that the main issue here is that the power dissipation
formula that we all know and love and teach to our students assumes
perfect transmission of sound through the atmosphere, which is a very
bad assumption. The fact that we use exactly the same formula for
light in vacuum and sound in the atmosphere should key us into the
fact that something is likely not well represented in the formula.
Assuming that the power dropoff depends only on the distance using the
usual formula is no better (at large distances anyway) than assumping
the same dropoff for light as you increase the distance from a lamp
during a dust storm.
In the case of sound, in particular, relative humidity has a
substantial impact - temperature too. The attenuation from these
factors alone can additionally dissipate tens of decibels per 100
meters... so it cannot be neglected in general if distances become
very large.
Todd
On Fri, Apr 5, 2013 at 12:21 PM, Dr. Richard Tarara
<rtarara@saintmarys.edu> wrote:
The answers from the two Johns are useful, but the bottom line is that inlarge
theory the distance is NOT unreasonable. A way to think about it is to
imagine outer space filled with wind free air (OK--no longer outer
space....but) and now do the experiment. The key here is the large ratio
between the initial sound intensity and the intensity at the threshold of
hearing. Even at inverse square fall-offs, it still requires a very
spherical surface to reduce the intensity by 10-12 orders of magnitude.drop
R.W.Tarara
On 4/5/2013 2:00 PM, Anthony Lapinski wrote:
I was considering this sound problem.. For a 100-W megaphone, how far
would you have to be so that it is barely audible (0 dB)?
I = P/A
Io = P/4pir2
With Io = 10-12 W/m2, the result is 2821 km = 1750 mi
This seems unreasonably far! I would think that the sound level would
off much closer, as we typically experience. Or am I
missing/miscalculating something?
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Richard Tarara
Professor of Physics
Saint Mary's College
free Physics instructional software
www.saintmarys.edu/~rtarara/software.html
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--
Todd K. Pedlar
Associate Professor of Physics
Luther College, Decorah, IA
todd.pedlar@luther.edu
or pedlto01@luther.edu
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