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Re: [Phys-L] sound intensity problem



The issue is not with the transmission, but in the conversion of electric
to acoustic energy. A 100 W megaphone is rated by the electrical power
needed to operate it. Speakers are only 2 - 5% efficient. If you take
that into account, your estimate of loudness with respect to distance will
be more realistic.

Steve Gollmer
Dept Science & Mathematics
Cedarville University


On Fri, Apr 5, 2013 at 3:42 PM, Todd K. Pedlar <todd.pedlar@luther.edu>wrote:

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 in
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
large
spherical surface to reduce the intensity by 10-12 orders of magnitude.

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
drop
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


_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
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--
Todd K. Pedlar
Associate Professor of Physics
Luther College, Decorah, IA
todd.pedlar@luther.edu
or pedlto01@luther.edu
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l




--
Steven Gollmer
Dept. Science and Mathematics
Cedarville University