Far off cannons are heard but closer ones are silent
Cannons are loud. Before an interesting discussion with Tom Mulder, a DPhil student who studies how animals detect vibrations, I imagined that the further from a cannon you were the quieter it would be. This is not true.
This diagram summaries one of the figures in the entertaining and informative paper “Strange sounds in the atmosphere”. There is a silent zone about 100 km from the explosion which is about 100 km long!
It turns out that in this cartoon how quickly the gun goes quiet is also strange. If you assume the explosion is 150 dB from 10 meters away, then you should expect it to still be a perfectly audible 70 dB when 100 km away, assuming a uniform spherical spread. The reason you stop hearing it ties to another interesting sound fact. You can hear things from further away at night.
There are three ingredients to understanding this: refraction, sound speed and emissivity.
Refraction occurs when a wave changes speed moving from one medium to another. If the wave is moving into a material where it is faster it will bend towards the interface. If it is moving into a substance in which it has a slower velocity, its path will bend away from the contact surface.
Warmer air has particles that move more quickly than cold air. Those particles move into low and out of high density regions more quickly and so transmit sound faster. If the air close to the surface is warmer than the air above, sound will refract up and away from the surface.
Why is air near the surface cooler than the air above it at night? The emissivity (how well a material emits and absorbs infrared radiation) of the ground is much higher than the air. The ground heats up faster during the day and cools down more quickly at night. Warm surface and cold skies during the day, the inverse at night.
All together this means during the day sound from the explosion is refracted up into the sky and away from you. (At night it is refracted in a more horizontal direction and so you can still hear the cannon at 100 km.)
So, what would you conclude if you had been the first to hear about the silent zone result? (Pause here to avoid any spoilers.) It turns out this was our first clue of a certain feature of our atmosphere.
If we suppose that the sound is reflecting from some higher point in the atmosphere this would require the speed of sound to be greater than at the surface somewhere up above us. Requiring a region high above us warmer than the surface.
This counterintuitive conclusion was true! In fact, these experiments were the first pieces of evidence for the ozone layer.
The ozone layer is at a mean height of about 50 km. It is hotter than the surface due to the strong absorption of UV rays by ozone particles. It is this layer (and some other temperature inversions) that the sound of the explosion is reflecting off, allowing us to hear it 200 km away!
Ref:
Cook, R. K. (1962). Strange Sounds in the Atmosphere. Part I. Sound: Its uses and Control, 1(2), 12-16.
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