A Twitter exchange recently revealed that certain members of the small subset of science writers who were humanities majors, also have a shared taste for classic mysteries. They thought they would co-post, on their respective blogs, some nice literary analyses ("the epistolary opening of Busman's Honeymoon ..."), but then realized that readers were no doubt bored by the overuse of epistolary openings in the science blogosphere. So they decided to write about the science of classical mystery writers instead. Links to other posts in the series by Deborah Blum and Ann Finkbeiner -- plus me at Discovery News on Jane Langton's Dark Nantucket Noon, and here at Cocktail Party Physics on Dorothy Sayers' The Nine Tailors -- can be found at the end of this post.
Scotland Yard Inspector Alan Grant encounters an intense young man with tousled black hair and "reckless eyebrows" on a train en route to a holiday to Scotland in Josephine Tey's The Singing Sands. The young man is found dead when they reach the station, and Grant accidentally walks off with the young man's newspaper. He doesn't think much of it at the time, until he notices a half-finished poem scribbled in the margins of the newspaper:
"The beasts that talk,
The streams that stand,
The stones that walk,
The singing sand...."
While the lines aren't an especially impressive effort, Grant finds himself haunted by them, particularly the reference to singing sands. "Surely there actually were singing sands somewhere? It had a vaguely familiar sound. Singing sands. They cried out under your feet as you walked." That poem sets Grant off on a mission to uncover both the identity of the young man, and who might have wanted him dead.
Grant (and Tey) is not the first to find inspiration in the singing sands. That is also the title of a classic 1960s episode of Dr. Who, in which the time-traveling TARDIS crew crash-lands in the middle of the Gobi Desert and conveniently bumps into famed explorer/trader Marco Polo and his caravan on their way to the palace of Kublai Khan. At some point in the journey that ensues, they witness a strange desert phenomenon: singing sands.
Marco Polo did claim to have journeyed across the Gobi Desert, and said the dunes filled the air "with the sounds of all kinds of musical instruments, and also of drums and the clash of arms." His storied adventures took place in the 13th century, but accounts of singing, or booming (and sometimes squeaking) sand dunes date as far back as 9th century China. According to an ancient manuscript, people used to climb Mount Ming-Sha-Shan (now known as the "Singing Mountain") on a special festival day, and slide down the sand, producing the sound of rolling thunder. Centuries later, Charles Darwin commented on singing sands while traveling in Chile.
It's a fairly rare phenomenon. Only about 30 dunes worldwide are musically inclined -- the rest, apparently, are tone deaf -- although astronomers and geologists suspect that the sandy hills on Mars might also be alive with the sound of music. Popular folklore has blamed underground rivers or even genies; Marco Polo blamed evil spirits. (Image source)
Scientists have also puzzled over the phenomenon. There have been numerous hypotheses as to the cause, most centered on the notion that it comes from vibrations of the dune as a whole. For example, some surmised the effect was similar to how a violin bow moving across the strings produce a musical tone, with the sandy sounds coming from blocks of sand stick-slipping across the body of a dune. Another instrumental hypothesis likened the effect to how a flute produces a pure tone via resonating air in the hollow tube.
It turns out that neither of these hypotheses are correct: the phenomenon appears to be linked to the individual grains of sand acting in concert. See, sand is pretty fascinating stuff, from a physics standpoint. It's technically known as granular material, since it acts both like a liquid and a solid: dry sand collected in a bucket pours like a fluid, yet it can support the weight of a rock placed on top of it, like a solid, even though the rock is technically denser than the sand. So sand defies all those tidy equations describing various phases of matter, and the transition from flowing "liquid" to a rigid "solid" happens quite rapidly.
It's as if the grains act as individuals in the fluid form, but are capable of suddenly banding together when solidarity is needed, achieving a weird kind of "strength in numbers" effect. Per the folks at Physics Central:
"Granular materials form what are called 'collective' systems, because the particles' touching and rubbing together is so important in determining what happens. In a sandpile, for instance, each particle touches only a few others, but these 'short range' interactions determine what happens to the whole pile. In this sense, a sandpile could be a model for the behavior of, for example, cells in a colony or workers in an economy."
Here's what we do know about what's going with granular material. First off, you've got gravity pulling down on each single particle. You've also got friction between those particles as they interact; how much friction depends on how big the particles are, what they're made of, and whether they're suspended in water, for example. (There was a paper published just last month, in fact, about how the same equations that describe the fluidlike flow of granular material work pretty well for describing how a fluid's viscosity increases when suspended particles are added to the mix.) And of course, any time particles are moving and bumping around together, you've got mechanical energy being lost as heat, per the trusty laws of thermodynamics.
All those factors give rise to three primary mechanisms common to granular material: (1) percolation, in which small grains migrate down to the bottom of the pile between larger grains; (2) convection, in which larger grains push up toward the top of the pile; and (3) condensation, a kind of sifting mechanism discovered back in 2001 by Lehigh University's Daniel Hong.
These are the group dynamic mechanisms that, combined, give rise to the so-called Brazil Nut Effect: that annoying tendency for the biggest nuts (in a mixed nuts container) to rise to the top during transit. Somehow those always seem to be the Brazil nuts, which are nobody's favorite. The small nuts gradually migrate downward, the large nuts gradually rise to the top, although, as io9 points out, the density of said nuts, not to mention ambient pressure, can also be a factor:
If the large particles are much less dense than their surrounding particles, they rise to the top and stay. If they are much denser than their surrounding particles they also rise to the top and stay. Those that have a small difference in density from the other particles tend to remain mixed. And all this density dependence stops if the particles are in a vacuum. It seems that the simple course that a Brazil nut takes through life is dependent not only on its surrounding nuts, and on its density, but on air pressure as well.
A few years ago scientists at MIT and Clark University studied sand in a rotating drum, observing that the sand would build up into a pile and reach a steep slope before collapsing -- a smaller, lab version of an avalanche. The technical term is self-organized criticality, and it applies to all kinds of complex systems, including the flocking patterns of starlings.
Remember when I wrote about phase transitions and talked about the critical point where a material's phase changes from, say, a solid to a liquid, as with melting ice? Self-organized criticality is similar, except in one very important respect. In a conventional critical system, like melting ice, the phase change is achieved by varying a control parameter -- usually temperature or pressure.
With self-organized criticality, however, the critical point is reached independent of any particular control parameter. Instead, the driving mechanism is the intricate dynamics of the individual particles that make up the system, acting in concert. And a sand pile just happens to be the quintessential real-world example of this phenomenon.
Take, for example, an hourglass. The sand in the top part pours through the channel and drops to the bottom compartment, gradually building up into a pile. As the pile grows, avalanches occur which carry sand from the top to the bottom of the pile. At least in model systems, the slope of the pile becomes independent of the rate at which the system is driven by dropping sand. This is the (self-organized) critical slope detailed in the above image. (Image source.)
Here's a story I'm fond of telling when people ask me when I realized I was finally, really and truly, a science geek. I was riding a shuttle bus back to my hotel from a physics conference, where I'd listened to a press conference on the physics of granular media. We passed a construction site where a huge machine was dumping sand into a gigantic pile. As I watched, the sand pile peaked and "avalanched," as the sand redistributed into a shorter pile with a broader base and started building up to a peak again. I pointed and exclaimed to my seatmate: "Look! Self-organized criticality!"
There it was, right in front of me, making the seemingly obscure technical language of the press conference suddenly relevant to my everyday life. And I'm not alone. I recently chatted with a female physicist who specializes in fluid dynamics and granular media who found her way into the field because she'd always been fascinated by the intricate patterns she observed in the waves and the sand dunes as a child visiting the beach. "Eventually I realized that wasn't normal for a child. But by then I loved it too much to care." (Image source.)
Nor can physicists precisely predict an avalanche. That's partly because of the sheer number of grains of sand in even a small pile, each of which will interact with several of its immediate neighboring grains simultaneously -- and those neighbors shift from one moment to the next. Not even a supercomputer can track the movements of individual grains over time, so the physics of flow in granular media remains a vital area of research. (Among other agencies, NASA is funding work in this area.)
How does all of this this apply to singing sands? One international team of scientists -- hailing form the University of Paris, the CNRS Lab in Paris, Harvard University, and the Universite Ibn Zohr in Morocco -- have conducted field studies all around the world, supplemented with controlled lab experiments, and published their findings in Physical Review Letters. They found that the sounds come from the sliding motion of avalanche dynamics. (You can listen to the nifty sounds they recorded from sand dunes in China, Oman, Morocco and Chile here.)
The team stumbled on their insight a few years ago by accident while studying the formation of crescent-shaped sand dunes in Morocco. As they scrambled up a particularly steep dune, they set off an avalanche, producing a 100-decibel singing sound. And they found they could reproduce the sound by sliding down the dunes with their legs swung out. They took recordings back to the lab in France and managed to replicate the same sound in a donut-shaped sandbox.
Specifically, they were able to measure vibrations in the sand and air, thereby detecting surface waves emanating from the avalanche. According to head researcher Stephane Douady, the face of the dune seems to serve as a kind of loudspeaker and the surface waves produce the sound in the air. The waves result from collisions between individual grains -- about 100 times per second, according to the lab measurements -- that create a kind of feedback loop of synchronized collisions at a specific frequency, and voila! The dune begins warbling a sandy song.
It just so happens that if sand is packed tightly, it can't move without expanding its volume. Douady thinks that a dune avalanche serves to compress and decompress air among individual sand grains, and this causes the singing sound. In fact, the grains themselves are unique: round, with a coating of silicon, iron and manganese.
As a result of all this ongoing research, physicists now know that certain conditions must be met before you can get the singing sands effect. First, the grains of sand must be round, and of the right size (between 0.1 and 0.5 mm in diameter). The sand grains must contain silica, and the humidity has to be just right, too. When all those factors come together, a sand dune will emit those telltale "songs". We even know the most common frequency: 450 Hz.
Castles in the Sand
And there's more! The frivolous summer pastime of building sand castles also harbors some interesting physics. Everyone knows sand has to be wet to build sand castles -- just enough to cause the dampened grains of sand to stick together via surface tension. (Jen-Luc Piquant has experimented extensively and found that the perfect ratio for an optimum castle is one pail of water for every eight pails of sand.) The water forms "liquid bridges" between the contact points of the grains, and the resulting tension creates an attractive force between them.
Remember the physicists who experimented with sandpiles in the lab? They conducted their experiments with both dry and damp sand, and found that adding even a tiny bit of water made the grains stick to each other more effectively, so that the pile could reach steeper angles and collapse less drastically than when the sand was dry. And just like sand castles collapsing on a beach in clumps, some of the "bridges" in the experiment stayed intact.
You can build far more stable and intricate sand castle designs if you have a fundamental grasp of these basic principles. And if you're Arshad Kudrolli of Clark University, you can exploit the physics of granular media to build all kinds of unusual slender structures. He and his postdoc, Julien Chopin, have a new paper in Physical Review Letters on their experiments building so-called "granular towers," drop by meticulous drop.
They set up a dry bed of sand (or, in some cases, blotting paper) and slowly dripped a mixture of sand and water onto the surface. Normally, with just drops of water, the drops would splash, spread or bounce upon impact. But in this case, the liquid was absorbed by the surface, causing the sand particles to undergo a sort of "flash freeze" upon impact.
That gave Kudrolli and Chopin sufficient control to stack the drops right on top of each other in various intricate shapes, the particles held in place ultimately by a combination of friction and capillary forces. Considering how important the control of granular media can be in industrial applications like surface patterning, this work could end up being fairly significant. (Image source)
Speaking of real-world applications, we also have things like quicksand, a mixture of fine sand, clay and saltwater. At rest, it's little more than loosely packed grains of sand resting on top of water. But if some unfortunate soul happens to fall into quicksand and start flailing about, the movement transforms that delicate balance, turning it into a dense liquid soup.
This means the victim sinks deeper, at which point the the water and sand starts to separate again into water-rich and sand-rich levels. The wet sand sediment becomes densely packed, trapping the victim. Fortunately, the average density of a human body is about 62 pounds per cubic foot, much less than the 125 pounds per cubic foot of most quicksand. So the trick to survival, apparently, is not to panic. Instead, relax, stay still and stretch out on your back to increase your surface area, and then just wait until your legs pop free.
Studying quicksand could lead to insights into the shifting of wet soil underground during earthquakes that causes buildings to sink into the ground (soil liquefaction). The water-soaked soil "liquefies" because of the vibrations of the quake. The shock waves compress the soil faster than the water can escape, raising the pressure so that the water bears more of the load than the sand. And the buildings start to sink. For safety reasons, obviously scientists would like to understand this process better, perhaps developing better building foundations to prevent liquefaction.
Man, you think you know a substance, it's so familiar, you see it every day, but somehow it keeps surprising you with unexpected or inexplicable behavior. That's how some physicists feel about sand and other forms of granular materials. So the next time you're building a sand castle at the beach, or pass a construction site just when a sand pile hits the point of self-organized criticality, take a moment to appreciate the intricate complexity that can be found in that collection of millions of grains of sand.
Check out these related posts!
The Science of Mysteries: Instructions for a Deadly Dinner (Deborah Blum on Dorothy Sayers' Strong Poison)
The Science of Mysteries: Watch Where You Fall In (Ann Finkbeiner on Josephine Tey's To Love and Be Wise)
The Science of Mysteries: For Whom the Bells Toll (Jennifer Ouellette on Dorothy Sayers' The Nine Tailors)
The Science of Mysteries: Total Eclipse of the Heart (Jennifer Ouellette at Discovery News, on Jane Langton's Dark Nantucket Noon)
NOTE: This is an updated version of an earlier post that appeared on the old blog back in 2006.