Under optimal conditions, how far could an emergency whistle be heard?
Whistles are often used for emergency signalling, it would be good to know how far that signal can travel and still be recognized.
There are plenty of factors that would affect the distance, so how far would it travel under optimal conditions and then one could figure that real world conditions would be less.
As starting point,
- The world record unaided human whistle was recorded at 125 decibels at 2.5 meters
- Sport referee whistles go up to 127 decibels recorded at 2 meters.
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Practically, I don't know how far, but a lower pitch will generally carry farther. Also, one's hearing works better if the sound pattern is unusual or personally known to the listener. (A loved one's voice across a crowded party.) Fog horns are low pitched to reach farther. A ululating sound pattern is often used to catch one's attention. I like the sports type whistle with a free-traveling ball inside to warble. Also consider listeners: as we age our hearable frequency range shrinks.
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The simplest, as opposed to the optimal, approximation is to assume the inverse square law holds such that there is a 6 dB drop in the pressure for every doubling of distance. If we assume that the whistle needs to be 35 dB to be heard outside in this "optimal" scenario, the pressure needs to drop by 90 dB (or 15 doublings of distance). 2^15*2.5m is about 82 km. If it is really quiet and you have excellent hearing, maybe you could handle another 6 doublings or 5000 km.
There are a lot of factors that will affect the actual distance. With the right thermal layers, the atmosphere can act as a wave guide allowing sound to propagate 1000s of kilometers. While this seems far fetched, it is pretty common underwater. Wind, acoustic absorption, and scattering, will likely shorten the distance. Less acute listeners may need a whistle to be louder than 35 dB, especially if there is any background noise.
I touched on a number of these concepts in my answer about highway noise.
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