Waves may seem like a simple concept, but monsters are lurking beneath the surface
Show to kids how sounds can be transformed into water waves. It is a good start into the topic of waves, because as soon as you try to think of the inner processes that are driving a wave, you will face a series of challenges.
On Nov. 17, 2020, an oceanic buoy off the coast of Ucluelet on Vancouver Island in British Columbia detected a monster that has been a maritime folklore. At one moment, without warning, a freakish 17.6 meters tall wave appeared out of nowhere. It was three times higher than surrounding waves, the record-breaking size difference in sea waves. This monster is known as the rogue wave – a mysterious natural phenomenon that had been treated as an imagination of sailors until recently.
“Let’s talk about something simple, like waves”, I thought
Waves are ubiquitous. We tend to think of them as something trivial because we see them everywhere - in liquids all around us, in clouds, on stadiums as a “Mexican wave” (or just “the wave” if you are from the US), in legs of millipedes, in spread of infectious diseases, in colorful chemical reactions, in economy, in your arms when you try to make cool dance moves. We also know that some other things, like sound and light, are waves, but it takes extra effort to recognize them as waves.
And this extra effort was something I wanted to talk about. It is a good feeling when you start recognizing wave phenomena of light in everyday situations. My personal favorite is understanding how some animals, like beetles, get their beautiful extra-shiny colors. It seems natural then to start the story of waves with a simple question: what is a wave?
If you want to answer this question in a more general way, the assumed simplicity is deceptive. The word “wave” is so general that I would say it means “a pattern that is changing over time”. This pattern can exist in any kind of observed data, be it a physical medium (e.g., water or air) or a social construct (e.g., meme on a social network or price of gas). I would also categorize pattern changes into two groups:
The real wave is a traveling disturbance that caries energy and/or information: water molecules pulling on their neighboring molecules using their local electric field, or a person on a stadium observing his/her neighbor to decide when to stand up, or air molecules colliding off each other, or people sharing a meme with their friends on Facebook.
The illusive wave is an optical illusion: two disjoint parts of a medium perform some movement independently of each other, but they are in sync such that it looks like a moving pattern.
We typically think of waves in the first category, and this is what we will focus on now. The second category is often a matter of our brain picking up a pattern in random events because our brain is evolutionary hardwired to look for patterns (although, it took 50 years to prove recently that fireflies synchronizing their flashes is not an illusion). The illusive waves can be also created by combining real waves. Actually, mathematics tells us that any kind of pattern can be broken down into a sum of basic simple waves.
The important property of waves is that they do not transport the medium itself. This means that, for example, water or air molecules are pulled back and forth, but their average position remains the same. The medium can have an overall movement, but then we recognize this as a current (e.g., sea currents of water, wind currents of air, electric currents of electrons, human currents of daily commute to work).
Since the real waves transfer energy or information, we can only talk about the speed of this transfer along the direction of wave propagation. This is what we usually call the group velocity of a wave or the signal velocity. The basic law of nature is that the speed of transferring energy or information cannot exceed the speed of light. But problems can arise if properties of the medium influence the signal velocity and the shape of the wave, which leads to various wave phenomena at the boundary between two materials or within a material. The concept of group velocity might lose its meaning and an illusion of faster than light speed can arise. On the other hand, the illusive waves have no limits on what kind of illusionary speed of wave they can achieve (called the phase velocity) as they do not carry anything.
The importance of making waves
We will not go deeper into the problems of defining wave velocities for now. Instead, let’s keep things simple and give kids a visual demonstration of two types of waves and two types of reflections. For this we will use the classic unsurpassed toy for this purpose - Slinky:
Get a metal Slinky and attach one side to some fixed object (I tape it to a doorknob). We call this situation the “hard” wall.
Make a wave by compressing and releasing the Slinky. Observe how the compression travels back and forth through the Slinky. This is a longitudinal wave.
Make a wave by swinging the Slinky to one side. Observe how the deformation travels to the other end and how it reflects. This is a transverse wave.
Now attach the other end to a rope and attach the rope (at about arm length) to the wall (e.g., doorknob). This enables the Slinky’s end to move freely (so-called the “soft” wall). Make a transverse wave again and observe how it bounces back from the end.
This Slinky wave game is one of the key experiments that kids must try in any teaching course on waves. It is both visually pleasing and highly informative demonstration of wave propagation and their interaction with an obstacle. Notice how a hard wall forces the transverse wave to change its oscillating side, unlike in a soft wall where it bounces to the same side. This works for any wave, including light waves that we will cover in the future stories.
Monsters beneath the surface
Now, you can start looking for such a wave behavior around you in daily life. Of course, water waves come first to mind. But as Richard Feynman put in his famous physics lectures, “they are the worst possible example, because they are in no respects like sound and light; they have all the complications that waves can have”.
To navigate through these complications, we have to be more precise about what kind of a water wave we want to talk about here. The force acting on water can be surface tension (tiny “capillary waves” where surface molecules pull on each other by their molecular electric forces) or the weight of displaced water (so called “gravity waves”). These two types of waves display different group and phase velocities.
We focus on gravity waves here, which is what we typically mean by a water wave. If we follow the path of individual water particles within such a wave, we will notice that they move in circles, where the circle size drops with depth. Interestingly enough, this very same mathematical solution, called Gerstner wave, is used in computer graphics to create realistic rendering of water surfaces.
When waves shake hands
Another important property of waves is how they behave at the boundary of two materials of different properties for wave propagation. This will be very important in our future description of soap bubble colors. Interestingly, we can demonstrate this wave behavior using two Slinkies:
Take one plastic and one metal Slinky, and tape them together into one very long Slinky.
Attach one side to some fixed object (I tape it to a doorknob).
Make a wave and observe what happens when the wave passes over the boundary between Slinkys.
Now switch the fixed side and make waves again. Observe how the wave behavior changes at the boundary.
The plastic Slinky is lightweight and waves travel fast through it. The metal one is heavy and waves travel more slowly. When we make a wave on one side, it must travel over the boundary between the fast and slow medium:
If the wave comes from the plastic (fast medium) side, one wave of smaller amplitude will pass through into the metal part (slow medium), and one wave is reflected back from the boundary, but with the change of (left-right) side.
If the wave comes from the metal (slow medium) side, one wave of larger amplitude will pass through into the plastic part (fast medium), and one wave is reflected back from the boundary, but it does NOT change its (left-right) side.
This property of waves on the medium boundary is an important lesion that we will refer to when we will talk about light.
Making sounds visible
Many waves around us are detected by our senses, but not directly visible as waves. Sound is one of them. Fortunately, there is a simple and fun way how to turn sound into visible waves:
Take a loudspeaker (if you have a bass speaker, even better), point it upward, and connect it to your computer. Open this page and be ready to play it: https://pudding.cool/2018/02/waveforms/
Take a large empty plastic bottle and cut off the top and bottom part to make a plastic cylinder
Put the plastic cylinder on the loudspeaker, such that all the sound is captured and channeled by the cylinder
Experiment #1: Cover the top of the cylinder with aluminum foil. Play some music and try sounds from the above-mentioned link. Put little bits (beads) of Styrofoam on the foil and observe how they “dance”.
Experiment #2: Attach a tiny mirror to the foil (glue it because the vibrations tend to move it) and shine a laser onto it, such that the beam reflects to the wall. Play sounds from the above-mentioned link and observe the shapes that laser makes on the wall.
Experiment #3: This is messy, so better cover your loudspeaker with a plastic foil to protect it. Cover the top of the cylinder with a plastic foil. Do not stretch the foil too much, because now you need to put some water on this foil. It is easy to spill this all over, so be careful. Put some food coloring into the water to make it more visible. Play songs and sounds now.
Sound is a longitudinal wave propagated as air compressions. When such a wave hits a membrane (aluminum or plastic foil in our experiments; eardrum in case of your ear), variations in the pressure waves pull and push the membrane. We just need to make these membrane movements easily visible – and this is what these experiments are doing.
Waves also spread through solid material as vibrations and can travel large distances. Earthquakes are a dramatic case when the whole planet vibrates, but similar waves exist on the Sun and other stars, too. The Earth’s atmosphere is also a fluid, sitting on the planet’s surface thanks to gravity. It is hard to visualize in our head a planet’s atmosphere as a huge transparent low-density ocean. But nature sometimes creates events that are so colossal that the entire atmosphere becomes small in comparison. The Hunga Tonga-Hunga Ha‘apai explosive volcano eruption in January 2022 was such an event. It exploded with such a force that the plume of gas and ash reached the incredible altitude of 58 kilometers (36 miles) within tens of minutes after the explosion. The volume and pressure of the explosion was so enormous that it triggered a massive atmospheric wave visible in satellite images. The vertical air movement traveled as a wave around the globe. The wave disturbed the air properties such as temperature and water vapor, which made it visible in images, and moved the sea water, which created a tsunami all around the planet. It was like a giant hand had smacked the atmosphere and splashed the air. The “smash” created visible ripples in the atmosphere, like waves on water.