Storm in a Teacup: The Physics of Everyday Life(37)
I kneel down and stroke her back. All that running around has made her hot. She isn’t sweaty because dogs don’t sweat, but she still has to get rid of all that excess heat. The panting looks like hard work, presumably using lots of energy and generating even more heat. It seems like a bit of a paradox. Inca is untroubled by my ponderings but quite happy to be stroked, and a strand of saliva drips from her wide-open mouth. After I’ve been out running, my breathing rate comes down back to normal quite gradually, but when Inca stops panting it happens very suddenly. Big brown eyes look up at me, and I wonder how much longer she needs to recover before it’s time for more tennis balls.
By far the most efficient way to lose heat is to evaporate water. That’s why we sweat. Turning liquid water into a gas takes a huge amount of energy, and conveniently the gas then floats away, taking that energy with it. Since dogs don’t sweat, they don’t produce water on their skin that can evaporate, but they have plenty of water in their nasal passages. Panting is all about pushing as much air as possible over the wet insides of their noses, to get rid of heat quickly. As if to demonstrate the point, Inca starts panting again. I reckon she’s taking about three breaths each second, which seems like a lot of hard work. But the really clever bit is that it isn’t. Her lungs act as an oscillator. This is the most efficient rate for her to breathe at because it’s the natural frequency of her lungs. As she breathes in, she’s stretching the elastic walls of the lungs, and after a while, the elastic pushes back strongly enough to turn the cycle around. Just as the lungs get back to their unstretched size, she puts in a tiny bit of energy to send them off on the cycle again. The downside is that when she’s breathing this fast, she’s not really replacing the air deep in her lungs, so she isn’t actually taking on board much extra oxygen while all this is going on. That’s why she doesn’t breathe like this all the time. But just at the moment the need to lose heat trumps her need for oxygen, and by pushing her lungs at exactly the right frequency, she’s getting as much air through her nose for as little effort as possible. So the panting is generating a tiny amount of heat compared to what she’s losing. She’s breathing in through her nose, but she’s got her mouth wide open because the dribbling is also cooling her. When the saliva evaporates, that helps lose a bit of heat energy too. The panting stops again, and Inca eyes the abandoned tennis ball. One inquiring look at Campbell is enough (he’s well trained) and the game begins again.
The natural frequency of something depends on its shape and what it’s made of, but the biggest factor is its size. This is why smaller dogs pant faster. They’ve got tiny lungs, which naturally inflate and deflate many more times each second. Panting is a very efficient way of losing heat if you’re small. But it gets less efficient as you get bigger, and that may be why larger animals sweat instead (especially hairless ones like us).
Every object has a natural frequency, and often more than one if there are different possible patterns of vibration. As the objects get bigger, those frequencies generally get lower. It can take quite a push to make a really massive object move, but even a building can vibrate, very very slowly. A building can in fact behave a bit like a metronome, a sort of upside-down pendulum—the base is fixed while the top moves. Higher up, the wind is faster than at ground level, and this is enough to give tall narrow buildings the sort of shove that will start them swaying at their natural frequency. If you’ve ever been in a tall building on a very windy day, you’ve probably felt this. A single cycle can take a few seconds. It’s disconcerting for humans inside, so the architects of these buildings spend a lot of time working out how to reduce the swaying. They can’t remove it completely, but they can change the frequency and flexibility to make it less noticeable. If you feel it happening, don’t worry—the building will have been designed to bend, and it isn’t going to fall.
The wind may be gusty, but it doesn’t push in a regular rhythm that could match the building’s natural frequency, so there’s a limit to how bad the swaying can get. But the jolt of an earthquake sends out ripples in the ground, huge waves traveling out from the epicenter, slowly tipping the earth from side to side. What happens when a tall building meets an earthquake?
On the morning of September 19, 1985, Mexico City started to move. Tectonic plates underneath the edge of the Pacific Ocean, 217 miles away, ground over each other to generate an earthquake of magnitude 8.0 on the Richter scale. In Mexico City, the shaking lasted for three to four minutes, and it tore the city to pieces. It’s estimated that ten thousand people lost their lives, and massive damage was inflicted on the city’s infrastructure. Recovery took years. The US National Bureau of Standards and the US Geological Survey dispatched a team of four engineers and one seismologist to assess the damage. Their detailed report showed that a horrid coincidence of frequencies was responsible for a lot of the worst damage.
First of all, Mexico City sits on top of lake-bed sediments that fill a hard rock basin. The earthquake-monitoring devices showed beautiful regular waves with a single frequency, even though normally earthquake signals are much more complex than that. It turns out that the geology of the lake sediments gave them a natural frequency of oscillation, and so they had amplified any waves that lasted about two seconds. The whole basin had temporarily become a tabletop shaking at almost exactly one single frequency.
The amplification was bad enough. But when they looked at specific damage, the engineers discovered that most of the buildings that had collapsed or were badly damaged were between five and twenty stories high. Taller or shorter buildings (and there were plenty of both) had survived almost untouched. They worked out that the natural frequency of the shaking closely matched the natural frequency of the midsized buildings. With a long-lasting regular push at exactly the right frequency, these buildings had been twanged like tuning forks, and they didn’t stand a chance.