Re: [Phys-L] sound intensity problem

[John Denker <jsd@av8n.com>]

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.