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Re: [Phys-L] sound intensity problem

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)?

A useful reference is

I just spent a couple of minutes throwing together a numerical
model using a spreadsheet.

The attenuation is hugely dependent on frequency, as you would expect
based on kinetic theory, i.e. on the fact that air is made of atoms
with a nonzero mean free path. Viscosity and thermal conductivity
will "short out" the peaks and troughs, especially if the peaks and
troughs are relatively nearby.

The dependence on humidity is harder to figure, but still significant.

Under the most favorable conditions at 30 Hz, you should be able to
get a wave to go hundreds of km. Not thousands, but hundreds, which
is still kinda impressive.

At higher frequencies, the wave won't even go 1 km. There's a reason
why foghorns operate at low frequency. OTOH it was surprisingly late
in the game (mid to late 19th century) before people figures this out.

A short distances the non-dissipative 1/r^2 spreading dominates. At
larger distances the exponential dissipation dominates.

On top of that, you still need to worry about lensing and background