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# Re: [Phys-L] sound intensity problem

On 4/5/2013 1:00 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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I think the highlights of this paradox have been covered, if possibly in a half-hearted way.

Recall your personal observations. You have doubtless counted thousand one,
thousand two to estimate the distance of a thunder clap from the flash to the bang.

This is a line acoustic generator whose input can be 1 MV at 100 kAmps.
I assert you have never counted for more than a minute or ~12 miles.

You have witnessed Tonto during the course of the Saturday matinee, listening
for the iron horse, ear to the rail, though he could hear nothing via the air path.
You may even have verified this observation yourself.

Both of these results suggest that there is a significant transmission path loss
in the air path compared with other media.

You may not have been exposed to studies of bird navigation, which are fascinating!
One of the numerous modalities that birds employ is the infra-sound transmitted
from distant mountain peaks over paths of dozens of kilometers.... illustrating
the spectral variability of the path loss
(as well as the extreme pressure sensitivity of some avian ears.)

A final observation, concerning the electrical to sound transduction:
it was not unusual for an audio amplifier to be rated at 3 or 4 watts,
for noisy sound output levels, in the day; with
the growth of hi-fi hunger, acoustic over-damping was employed to flatten
the always colored spectrum of the moving cone speaker at the cost
of transduction inefficiency.

As it happens, a current feasibility demonstration uses a thin graphene membrane in an
electrostatic speaker arrangement provided by perforated silicon planar electrodes
which returns to high transduction efficiency levels thanks to its extremely light stiff membrane
which avoids coloration with just natural air damping of the very light structure over the
impossible 20Hz-20KHz target response.

Brian Whatcott
Altus OK