Showing posts with label physics. Show all posts
Showing posts with label physics. Show all posts

Tuesday, February 5, 2008

in case you were wondering

In case you're wondering why things have been so quiet on this site in the last few months, this figure shows the mood of your average PhD student as a function of time. It was generated by a friend of mine who just completed his degree in December after a long and courageous battle. The gray dot indicates my present location -- at least on the time axis.



But dammit it will all be over soon. And I hope that it will end on the "Woo!" side...

Wednesday, February 14, 2007

Ice Ice Baby

Another cool shot from NASA's Earth Observatory:


The image has 6MB worth of detail so you can really zoom in! This is a shot of the Sea of Okhotsk (which is between Siberia and Kamchatka for all the Risk players in the room). Cold arctic outbreaks, like those that put the Canadian prairies in deep freeze from time to time, cause intense cooling sessions over this sea. When the ice - which must be almost 100% pure fresh water for it to keep its crystalline form - removes fresh water from the sea, the enhanced saltiness of the water left behind is actually enough to cause that water to sink. This heavy water will sink to the bottom of the sea, and then cascade down into the deep ocean, like a slow motion water-fall. (Interestingly the same thing happens in the Mediterranean Sea because evaporation removes water but leaves salt behind.)

A neat feature of the image is that you don't really see clouds until the wind (which is blowing offshore) gets past the ice and starts blowing over the water.

Friday, January 19, 2007

The speed of light isn't really that constant

Okay, now this hit me like a sack of wheat. Somewhere, a long time ago it was ingrained in me that the speed of light is 300,000 kilometres per second. Einstein's theory of relativity is based on the concept that nothing goes faster than light. Once you convince yourself of that, you're off into the world of relativistic physics and you're almost ready to program satellites that need to be sent to Jupiter and beyond. You've bought into the concept that light always travels at the speed of light and that nothing can go faster than the speed of light.

So. I just learned that there are people out there that have been halting light. Now while I concede that you are always taught that 300,000 km/sec is the speed of light in a vacuum, and that it is slightly different in different media (hence Snell's Law), it is still pretty trippy to think that in certain media it is slowed to a snails pace. (Can you imagine light going at under 40 miles per hour? You could pass it on the highway...C'mon light! Step on it or get out of the passing lane!)

The application of this concept is that if you can harness light, you can essentially label atoms for microseconds which is apparently long enough for the information to be used as a quantum microchip. If this ever falls into practice, it would be like handing a calculator to a guy trying to calculate the squareroot of 23409 on an abacus.

...

Oh no, I think I'm experiencing a majorly nerdy geek bomb...

Thursday, January 18, 2007

What happens when you pluck the ocean?

Have you ever wondered why A440 sounds different on a piano compared to a violin? And then different again on a flute? Well, the short answer seems awfully simple and almost stupid: it's because the instruments make different sounds.

Anybody who has ever played a violin or a guitar or any other string instrument has probably noticed that there are two main things that affect what note comes off a string when you pluck it: the string length and the string thickness. When you pluck the string, the sound you get is due to how the string vibrates, and then how that vibration resonates within the instrument. Most of what you hear is the pitch of the note you plucked. But the richness of the tone of the instrument, that stuff that makes the violin sound different from the guitar, is due to all the other sounds that also resonate.

The exact physics of that difference in sound becomes very complicated very quickly. For example, most violins look more or less the same, but can sound drastically different from one another. It is because of subtle differences that every violin sounds different. Science describes these differences using tools called eigenvalues and eigenvectors. If you took first year Algebra in university you were probably exposed to these things, and you probably hated them.

In a nutshell, the reason instruments sound different from one another is because when you play a note, a whole bunch of other sound waves (lets call them modes) are also emitted from the instrument when it resonates. Which other sound waves (modes) are excited, and how loud they are relative to one another, is what makes a piano sound different from a squealing toddler. As luck should have it, these modes must obey the rules of some specific mathematical equation. Solving the equation may be quite simple for something like a drum, but can get very complicated for something like a violin. This is because the equation takes into account the shape of the object and its composition (e.g. if it is made of plastic or wood or crystal). Not just any random mode will satisfy the equation, only very specific ones do. These very specific modes are called eigenvectors and each one has an eigenvalue associated with it.

If you ever saw the movie the Red Violin, you might remember scenes where million-dollar isntruments are being tested with equipment resembling oscilloscopes. The scientists there would basically be examining how the instrument resonated, or in science-babble they would be determining what its eigenvectors were.

Q: So why are you writing all this, who cares, and what does it have to do with the ocean?

Well, often when people ask me what I do, I have a hard time explaining it. On the bus home yesterday I came up with an analogy to plucking strings on an instrument. Lately I've been fitting my ocean data to the eigenvectors of the Saint Lawrence Estuary near Tadoussac. You see, the tides "pluck" the ocean at specific frequencies, but then physics causes all these other waves to resonate as well. The speed and shape of the resonated waves are governed by the eigenvalues and eigenvectors of the water column, constrained by Newton's second law and the assumption that matter is not created or destroyed. By knowing which eigenvectors to look for, I've been trying to find specific waves in my data, separate them from everything else in my data, and then figure out which bloody direction they're going.