Water Waves

Chances are you've been to a beach before, and it's quite likely that there were waves whether you were at the ocean, a lake, or some other sizeable body of water. If you've ever watched the waves for a while, you might have noticed that they tend to arrive parallel, or nearly so, to the shoreline. Even if they are at angle when they are far away, they still reach the shoreline nearly parallel. Why? Another thing noticeable to anyone who has watches waves, and is visible in the above photo, is the crashing and "breaking" of waves as them come towards the shoreline. How does that happen?

The first question can be answered by fluid dynamics. In shallow water, that is at a depth which is smaller than the wavelength (measure of distance between wave crests), the speed of the waves depends on the water depth and gravity only. Specifically, the speed is equal to the square root of gravity times depth. This tells us that waves will move slowest in the shallowest water. Let's assume that there is a nice downward slope as you move away from the shoreline. Start by imagining a wave that begins parallel to the shore. As it moves closer, the shallower water will cause it to slow down. Now, what happens if the wave is rotated so that it starts at an angle to the shoreline?

If you think of the wave crest as a straight line, one end will be closer to shore than the other if it's at an angle. The far end is in deeper water and will travel faster than the shallow end. This causes the wave crest to turn until both ends are at the same depth or it hits the shore (whichever comes first). If you're having trouble imagining this scenario, try thinking about an axle with a wheel on each end. If you move both wheels at the same speed, the axle will move in a straight line. What happens if you hold one wheel stationary (more or less) and move the other? The moving wheel will rotate around the other one. Now, allow both wheels to turn but move one a little faster than the other. The axle will move forward while also gradually turning. This is analogous to our wave scenario.

That's one question answered, so on to the next one: what causes waves topple over? It may seem strange but this answer relies on the same principle as the first one. In this case, we can no longer treat the wave crest as just a line; it does have a finite width, after all. Since the back of the wave is in deeper water than the front, the back will travel faster and eventually catch the front. The water particles will accumulate behind the crest until it reaches a point when the added water forces the wave to topple over. If the wave is large enough, you may notice how the top rolls over the bottom. As water piles up behind the wave, the water becomes even deeper than the water in front. Consequently, the water in back moves even faster, particularly that on the surface. This helps the top of the wave crest to roll as the wave topples over. Keep in mind, however, that this is only valid for waves in shallow water. It's not often that you see breaking waves in the middle of a lake, partly for this reason. When you do see them, the wind is generally very strong and helps force them to topple over.

Fortunately, these are easy things to go see for yourself, so get out and enjoy the coming summer. Maybe the next time you find yourself at a beach, you'll pay a little more attention to the waves.


References
Waves in Fluids (video) by National Committee for Fluid Mechanics Films (1960s; more here)

Sonoluminescence

I believe the credit for this one goes to my lab partner.

At first sight, those three little pin-pricks of light may not seem very spectacular. However, the phenomenon that creates them (sonoluminescence) is really quite interesting. Some scientists once believed that the light was created by the ever elusive nuclear fusion, although this idea has since been almost completely rejected. We can get to the basic idea by breaking apart the name, sonoluminescence. The "sono" refers to sound, while "luminescence" is the glow. In essence, the lights are created by sound.

In the experiment above, we start with a rectangle container filled with purified water. The metal cylinder at the top that sticks into the water is a transducer; in other words, it will create the sound for us. Sound is a pressure wave; when it travels through the water (in this case), it causes the water molecules to oscillate back-and-forth causing regions of compression, where molecules are pushed together, and rarefaction, where particles are pulled away. The sound that we used was a higher pitch than humans can hear, known as ultrasound. If the frequency of the sound (that is, how many times it oscillates per second) is chosen correctly, a standing wave will form in the water. If you and a friend each hold one side of a rope and shake it in sync with one another, a standing wave will form. You'll know when one forms because there will be at least one point on the rope that doesn't seem to move. The stationary point is called a node. Between each node is an anti-node, the point that has the most motion. The anti-node is what we're interested in.

The next step is to make a very small bubble very near the anti-node. It is a difficult task, but if done correctly, the bubble move into the anti-node and get trapped there. Because the anti-node is where the wave motion varies the most, this point will rapidly oscillate between a high pressure state (compression) and a low pressure state (rarefaction). During the high pressure state, the air in the bubble will be squeezed into a smaller volume. The opposite happens during the low pressure state; that is, bubble's volume grows and the air inside can spread out more. This should help to explain why it is so difficult to trap a bubble. If you squeeze or stretch it just a little too much, the bubble will pop forcing you to start over.

So, we have a bubble in water that is changing volume due to being trapped in an anti-node of a sound wave. Now that the experiment is set-up, we can move to our initial question: why does the bubble light up? This is a difficult question to answer and, frankly, the exact answer remains a mystery of physics. However, we can make measurements that give us some insights into the process and allow us to speculate on what it could be. The light is emitted when the bubble is squeezed. At this point, the volume that air molecules have is very small. When the bubble is squeezed, the air molecules heat up. In essence, this heat causes the molecules to emit light. What isn't known is the process through which the light is emitted. The most accepted idea is that the heat energy pulls the molecules apart. When the molecules re-form, they emit light. However, this does not explain the spectrum (or variety) of light emitted. As the experiments continue, scientists hope to one day find the answer.

While this is a very neat experiment, it might not have much practical use. However, sonoluminescence does occur in nature. Have you ever heard of the beautiful mantis shrimp? Perhaps you've seen the comic about it that's been getting passed around lately. The mantis shrimp can close its claw so quickly that it creates a high enough pressure wave to form a cavitation bubble that can glow by sonoluminescence. Just be careful if you go looking for one. Not only do they create a large enough pressure wave to kill their prey, but it is even strong enough to break through the glass of an aquarium.


References and Further Reading
The Sonoluminescence Process by the American Institute of Physics
Sound is a Pressure Wave by The Physics Classroom
Sonoluminescence: Sound into Light (Scientific American article) by Seth Putterman
Mantis Shrimp by Chesapeake Bay Program
Why the Mantis Shrimp is my new favorite animal by The Oatmeal