The sound of thunder

Last Sunday (April 14) we had a series of thunderstorms roll through the region, kind of unusual for upstate New York at this time of year.  We're not particularly stormy in general, but most of the thunder and lightning we do get comes in the heat of midsummer.  On Sunday, though, a warm front brought in turbulent, moist air, and we got some decent storms and rain for most of the day.

At 11:51 AM (EDT), though, something odd happened.  There was a deep, shuddering rumble that repeated three times within the span of about two or three minutes.  (The first was the strongest.)  I grew up in the Deep South, where thunder is a frequent occurrence, and to my ears this didn't feel or sound like thunder.  Immediately I thought of a mild earthquake -- primed, of course, by the April 6 quake, centered in New Jersey, which was felt over large regions of New York and the neighboring states.

The rumble we experienced preceded the arrival of the strongest of the storms; because of that, and the fact that it "sounded wrong," I was convinced that we'd experienced an earthquake.  That conviction intensified when reports began to pour in that the same noise had been heard at the same time -- in locations separated by fifty kilometers or more.  (Thunder ordinarily can only be heard about fifteen kilometers from the source.)  

My wife, on the other hand, was absolutely sure it was thunder, albeit rather powerful and deep-pitched.

Well, let it never be said that I won't admit it when I'm wrong.

I started to doubt myself when the Paleontological Research Institution in Ithaca (only ten miles from my home) reported on Monday morning that despite numerous people calling in to report noise and shaking, their seismometer had not recorded an earthquake.  That seemed pretty unequivocal -- and after all, there had been storms in the area, even though at the time we heard the rumble, the center of the front wouldn't arrive for over an hour.  But if it had been thunder, how had a single thunderclap (or three in rapid succession) been heard over such a great distance?

The answer turns out to be a temperature inversion.  Ordinarily, temperature decreases as you go up in altitude; but this effect competes with the fact that cool air is denser and tends to sink.  (This is why in winter, the greatest risk of frost damage to plants is in isolated valleys.)  So sometimes, a wedge of warm air gets forced up and over a blob of cooler air, meaning that for a while, the temperature rises as you go up in altitude.

This is exactly what happens in a warm front; the warm air, which carries more moisture, rises and forms clouds (and if there's enough moisture and a high enough temperature gradient, thunderclouds).  But this has another effect that is less well known -- at least, by me.

The difference in density of warm and cool air means that they have different indices of refraction -- a measure of how fast a wave can travel in the medium.  A common example of different indices of refraction is the bending of light at the boundary between air and water, which is why a pencil leaning in a glass of water looks kinked at the boundary.  At a shallow enough angle, the wave doesn't cross the boundary at all, but reflects off the surface layer; this causes the heat shimmer you see on hot road surfaces, as light bounces off the layer of hot air right above the asphalt.

Sound waves can also refract, although the effect is less obvious.  But that's exactly what happened on Sunday.  A powerful lightning strike created a roll of thunder, and the sound waves propagated outward at about 343 meters per second; but when they struck the undersurface of the temperature inversion, instead of dispersing upward into the upper atmosphere, they reflected back downward.  This not only drastically increased the distance over which the sound was heard, but amplified it, changing the quality of the sound from the usual booming roll we associate with thunder to something more like an explosion -- or an earthquake.

So despite the jolt and the odd (and startlingly loud) sound, we didn't have an earthquake on Sunday.  I'm kind of disappointed, actually.  I didn't feel the one on April 6 -- although some folks in the area did -- and despite having lived in a tectonically-active part of the country (Seattle, Washington) for ten years, I've never experienced an earthquake.  I'd rather not have my house fall down, or anything, but given that the pinnacle of excitement around here is when the farmer across the road bales his hay, a mild jolt would have been kind of entertaining.

But I guess I can't check that box quite yet.  Thunder, combined with a temperature inversion, was all it was.

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It's all becoming clear

The phenomenon of transparency is way more interesting than it appears at first.

I remember thinking about the concept when I was a kid, the first time I watched the classic horror/science fiction film The Invisible Man.  Coincidentally, I was in high school and was in the middle of taking biology, and we'd recently learned how the human eye works, and Claude Rains's predicament took on an added layer of difficulty when it occurred to me that if he was invisible -- including his retina -- not only would we not be able to see him, he wouldn't be able to see anything, because the light rays striking his eye would pass right through it.  Since it's light being absorbed by the retina that stimulates the optic nerve, and Rains's retinas weren't absorbing any light (or we'd have seen them floating in the air, which is kind of a gross mental image), he'd have been blind.

So an invisibility potion isn't nearly as fun an idea as it sounds at first.

It wasn't until I took physics that I learned why some objects are transparent, and why (for example) it's harder to see a glass marble underwater than it is in the air.  Transparency results from a molecular structure that neither appreciably absorbs nor scatters light; more specifically, when the substance in question has electron orbitals spaced so that they can't absorb light in the visible region of the spectrum.  (If not, the light passes right through it.)  Note that substances can be transparent in some frequency ranges and not others; water, for example, is largely transparent in visible light, but is opaque in the microwave region -- which is why water heats up so quickly when you put it in a microwave oven.

The second bit, though, is where it really gets interesting.  Why are some transparent objects still clearly visible, and others are nearly invisible?  Consider my example of glass in air as compared to glass under water.  You can see through both, but it's much harder to discern the outlines of the glass underwater than it is in air.  Even more strikingly -- submerge a glass object in a colorless oil, and it seems to vanish entirely.

The reason is something called the index of refraction -- how much a beam of light is bent when it passes from one transparent medium to another.  A vacuum has, by definition, an index of refraction of exactly 1.  Air is slightly higher -- 1.000293, give or take -- while pure water is about 1.333.  The key here is that the more different the two indices are, the more light bends when crossing from one to the other (and the more the light tends to reflect from the surface rather than refract).  This is why the boundary between air and water is pretty obvious (and why those amazing photographs of crystal-clear lakes, where you can see all the way to the bottom and boats appear to be floating, are always taken from directly overhead, looking straight down; even at a slight angle from perpendicular, you'd see the reflected portion of the light and the water's surface would be clearly visible).

Likewise, the more similar the indices of refraction are, the less light bends (and reflects) at the boundary, and the harder it is to see the interface.  Glass, depending on the type, has an index of refraction of about 1.5; olive oil has an index of 1.47.  Submerge a colorless glass marble in a bottle of olive oil, and it seems to disappear,

The reason all this comes up has to do with the evolution of transparency in nature -- as camouflage.  It's a pretty clever idea, that, and is used by a good many oceanic organisms (jellyfish being the obvious example).  None of them are completely transparent, but some are good enough at index-of-refraction-matching that they're extremely hard to see.  It's much more difficult for terrestrial organisms, though, because air's lower index of refraction -- 1, for all intents and purposes -- is just about impossible to match in any conceivable form of living tissue.

Some of them come pretty close, though.  Consider the "skeleton flower," Diphylleia grayi, of Japan, which has white flowers that become glass-like when they're wet:

The transparency of the flower petals is likely to be a fluke, as it's hard to imagine how it would benefit the plant to evolve a camouflage that only works when the plant is wet.  An even cooler example was the subject of a paper in the journal eLife last week, and looked at a group of butterflies called (for obvious reasons) "glasswing butterflies."  These are a tropical group with clear windows in their wings -- but, it turns out, they're not all closely related to each other.

In other words, we're looking at an example of convergent evolution and mimicry.

The study found that some of the clear-wings are toxic, and those lack an anti-glare coating on the "windows."  This makes the light more likely to reflect from the surface, rather than pass through; think about the glare from a puddle in the road on a sunny day.  Those flashes of light act as a warning coloration -- an advertisement to predators that the animal is toxic, distasteful, or dangerous.

The glasswing butterfly Greta oto of Central and South America [Image is licensed under the Creative Commons David Tiller, Greta oto, CC BY-SA 3.0]

The coolest part of last week's paper was in looking at the mimics; the species that had the transparent windows but weren't themselves toxic.  Unlike the toxic varieties, those species had evolved anti-glare coatings on the windows, so the mimicry was obvious in bright light -- but in shadow, the lack of glare made them seem to disappear completely.  In other words, the clear parts act as a warning coloration in sunshine, and as pure camouflage in the shade!

Even more amazing is that a number of only distantly-related species have stumbled on the same mimicry -- so this particular vanishing act has apparently evolved independently more than once.  A good idea, apparently, shouldn't just be wasted on one species.

So that's today's cool natural phenomenon, which I hope I've clarified sufficiently.  There seems truly to be no end to the way living things can take advantage of physical phenomena for their own survival -- as Darwin put it, to generate "endless forms most beautiful and most wonderful."

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It's kind of sad that there are so many math-phobes in the world, because at its basis, there is something compelling and fascinating about the world of numbers.  Humans have been driven to quantify things for millennia -- probably beginning with the understandable desire to count goods and belongings -- but it very quickly became a source of curiosity to find out why numbers work as they do.

The history of mathematics and its impact on humanity is the subject of the brilliant book The Art of More: How Mathematics Created Civilization by Michael Brooks.  In it he looks at how our ancestors' discovery of how to measure and enumerate the world grew into a field of study that unlocked hidden realms of science -- leading Galileo to comment, with some awe, that "Mathematics is the language with which God wrote the universe."  Brooks's deft handling of this difficult and intimidating subject makes it uniquely accessible to the layperson -- so don't let your past experiences in math class dissuade you from reading this wonderful and eye-opening book.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]