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Re: [Phys-L] sound intensity problem

• From: John Denker <jsd@av8n.com>
• Date: Fri, 05 Apr 2013 11:41:00 -0700

On 04/05/2013 11:00 AM, 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?

The short answer is I don't know. However, here are a few
hypotheses to consider.

Let's suppose the numbers are right in theory. So the
question boils down to why this conflicts with common
experience.

1) A hypothetical answer is that the threshold of hearing
number applies only in a super-quiet room. In any outdoor
setting, a low-intensity sound gets drowned out.

In other words, it's the same reason why you can't see
stars in the daytime. The star is plenty bright enough
to exceed the nominal threshold of perception; it just
gets drowned out.

You can do the calculation on this, comparing the sound
of interest to ambient noise. I'll bet the latter is a
lot bigger than 1e-12 W/m^2.

2) Lensing. The temperature profile in the atmosphere is
such that sound "rays" get bent upwards. That means if
you are on the surface, you cannot hear things emitted
from the surface, because you have no line-of-sound to
the source.

OTOH if you are up in a balloon, you can hear sounds
from amazingly far away.

On the other side of the same coin, if you're on the
ground, you can hear a noisy airplane from amazingly
far away.

3) Other stuff I haven't thought of.

4) Combinations of the above.