In January, the world experienced the loudest bang of the century – and that of the previous century as well. The sound wave of Hunga Tonga was heard across the Pacific ocean in Alaska. The air pressure wave traveled around the world – and again. And again. The ocean wave caused a tsunami across the Pacific, with devastation on nearby islands and damage in Japan and South America. And all this from a volcano we had never heard about.
There is a common denominator in these three effects. This volcano made waves – and it was very very good at it. We are more used to associate waves with earthquakes. Like the sounds of Hunga Tonga, their waves traverse the Earth and are detected everywhere. The whole world rings after a major shake. Hunga Tonga gave us a reason to delve into the archives, and find what we had written about waves, to learn from ourselves. This post is based on one we ran in 2014, in the heady days of the months before Holuhraun. We let Carl speak, with some updates.
This post is about waves, how they happen, how those waves travelling, and how they are seen. In a way it is not about earthquakes or volcanoes at all, and not even really about sound, instead it is about the strange and wonderful world of waves. A field I have spent 20 years studying and researching.
One thing I have noticed is that even though sound waves are all around us all the time, and even though they rule our daily life in the most fundamental ways, very few really know about them and they are rarely if ever studied in schools. I think this is a pity, because out of the humble little sound wave you can derive everything in the universe. And I really mean everything.
But let us not venture out into quantum physics or plucky string theory; instead let us keep to our mutual shared interest of earthquakes and volcanoes. But, as with everything else we need to start at the beginning.
What is sound?
According to physics, sound is a vibration that propagates as a mechanical wave, while moving through a medium such as a gas (air), a fluid (water) or a solid (rock). It is one of many types of waves. They all have in common that they leave nothing behind. Once the wave has passed, the vibration stops. The net effect of a wave will always be a zero displacement. At sea, after a wave has passed, the surface goes back to how it was before the wave. A bird floating on the water will still be in the same place. The wave passes but the water stays behind. Think Mexican wave: the wave moves, the people remain, sitting still again.
To detect a wave we often need specialised equipment. For sound, may it be a violin or an earthquake rumble, it can be our ear, sensitive but imperfect. And it is also good to remember that the sound we hear is interpreted by our brains and may not always be as accurate as we tend to believe, and to complicate things even more, our ears are not that great. For recording we use the equipment of a studio or a seismograph. But, now I am getting ahead of myself again.
Back to the thing with wave propagation and media
There is a difference between waves moving in gases such as air and fluids like water, as in comparison to a solid. Mechanical waves within air and water almost to a flaw move as longitudinal waves. I will get back to longitudinal wave and its estranged cousin the transverse wave.
As the sound source vibrates it creates vibration in the adjoining media (often the air or water). This in turn creates pressure against the individual atoms. The atoms are pushed in a direction away from the point of origin; this creates excess pressure ahead of it (the atoms there resist being pushed), and the atoms are forced back. For the poor atom the movement will thusbe following the direction of the waveform, forth and back. This is important since it means that the mechanical energy will be following a longer distance (and slower) than the straight road. So, one could see it as the sound is travelling along an undulating road from the starting point.
A side effect of this is separation of frequencies over distance since a low frequency travels along a bigger undulation compared to its brother the high frequency component. This is though almost never a problem since high frequencies do not travel as far as low frequency components. Ahem, once again getting ahead of things.
Waves and energy
Now, nature seems to abhor leaving things dangling with excess energy, and a displaced atom will want to go back home, and it will do so in a rather mystifying progression. Well, if you have been a child born in the time where there were swings you will know the solution to the mystery by the seat of your pants, literally.
If we look at a wave as a discrete function it will move from 0 to 1 and one would then assume it would be happy at being back home at 0. But that is not true since the atom would at the end of the movement backward be going at full speed (think about how a swing behaves and what would happen if the swing came to a crash halt at the bottom with you on it), no, instead the atom moves happily onwards from 0 to -1 and then back to 0 as resting place. Now if you sum up the energy states 0, 1, 0, -1 and 0 you get a big fat 0 net motion of the poor atom. Natural longitudinal waves always have a net 0 energy value on the local scale. They leave no energy behind. The energy in the mechanical wave moving in a direction from the source. Think of the bird sitting on the water as the wave comes past. For a brief while the bird on the water moves energetically up and down, but then the bird comes back to rest and its energy is passed on downstream. The wave carries movement and energy with it, but leaves the matter behind. This might actually be the most fundamental part of our understanding of the Universe: energy and matter do not need to travel together.
Now a solid can suffer from another type of wave, the transverse wave, but we will get back to that one later. What is true for the longitudinal wave is also true for the transverse wave, it just has an extra step that is quite profound, but I will let that dangle until later.
Now a last thing about the medium. The wave will form due to the properties of the origin (a drum, violin or an earthquake) and that will give the waveform, but after that it is the medium that Rules the Waves. Speed, longevity and a lot of other factors govern how the wave will conduct through the media and how it will be transformed due to diverse diffraction and filtering functions. But, that, my friends, is beyond today.
You may feel this is enough for today. This article is based on a series of lectures I used to give as an introductory course to wave propagation theory in physics. Rest assured, I will not hand out assignments and there will not be a test at the end. This is my field and I tend to think about it in the form of mathematical formulations and technical jibber-jabber. I do hope that you all in the end will feel that you have gained a new understanding about seismographs and how they detect distant sounds from earthquakes. And, if I really succeed well I might even give a glimpse of my deep rooted love of physics, the Universe and how waves can help you understand everything.
Ready? Let’s move on.
Leave your sineful ways behind
It has been suggested by another of the editors that people enjoy images of cats and that if I posted one such it would keep the interest up for this dry series.
The cat in question did not like the Haiti earthquake. The cat in question has doubts about this.
In the first part I told a blatant lie. I thought the other editors would catch me, but alas not. The lie was put in on purpose so that I would have a point to start the next wavy part with. In short, I wrote that there are only 4 basic audio waveforms, and it was once believed to be true. But nowadays we know that all audio waveforms consist of the humble sine wave (or it’s cousin the cosine). So in a sense of it you have only ever heard one thing in all of your life.
Why now is that true? Well, let us just say that we can create all other waveforms from adding sine waves together according to specific “recipes”. I could either spend 3 pages on explaining this, or we just watch a brief video. After all, “what you hear is what you believe”. Video by Matt Mayfield from the Audio Kitchen.
In normal life you will basically only hear the sine wave, and the sine wave rules the longitudinal wave as we learned in part one of this series. As I mentioned last time the longitudinal wave travels as a mechanical sine wave and that it is the only possible way an audio wave can travel inside gas or fluid media. There are a couple of exceptions but we can leave those behind.
The sine wave has a close relative: it’s cousin the cosine. It is just like the sine, with one fundamental difference. A sine wave starts at rest, at zero displacement. It is a swing starting at the bottom. The cosine starts at maximum: it is a swing starting at the top. The sine and the cosine is in a way the same conundrum as the classical, “which came first, the hen or the egg?”
How does a sound wave start? It starts with something moving, for instance an explosion. This starts of the wave. Thus the sound wave in the air or the water starts out as I that seductress of wave physics, the cosine wave, with the initial excursion of the swing coming from the whatever caused the sound: a drum, a cat, a volcano. The cosine carries the sound of the earthquake.
But in solid media there is another type of mechanical audio wave lurking in the shadows and it travels as something called a transverse wave.
Transverse and longitudinal waves
In a sound wave the atoms move forward and back in the direction in which the wave is moving. It alternates as a compression and a dilution while traveling in that direction. This is what sound does, and what makes the thingies in your ear move, wave, and produce electrical signals towards your brain which make you ‘hear’ the sound. These waves are called ‘longitudinal’.
But waves do not have to travel this way. The can also move things on the ways sideways (transverse) while traveling in another direction.
As people set up new sciences they tend to want to differentiate themselves from the parent discipline. They use different names and expressions. In physics it is a transverse wave, whilst in Geologese it is a seismic S (secondary) wave. But basically it is the same thing with a different name.
The two most often occurring versions of transverse waves are the planar transverse wave (mega-thrusts produce these for instance) and the rather beautiful spherical transverse wave. One does not need to be a genius to understand why these waves really go heavy on buildings, one functions as a jolly trampoline and the other will twist the house upwards and sideways before the house is unceremoniously dumped back on the ground.
What is happening in the last animation is that the circular motion of the cosine is creating an expanding spiraling wave; this means that the sound from the earthquake will be immediately separated into two distinctly different components with one wave travelling almost straight to the observer, and the second will be travelling a much longer way.
Think of it like this, you have one fireman named Mike Ross sliding down a fireman’s pole and another fireman named Mike Ross running down a spiral staircase, both Mikes are of course starting at the same time. The poling Mike Ross will come down before the transverse (spherical) spiral staircase Mike Ross even if they travel at the same speed. This is due to the spiral staircase being representative of a longer route to the finish line.
If you want to experiment on your own you can go outside and tie a rope to a tree, if you move your hand up and down you will see a planar transverse wave wandering down the rope, and if you move your hand in a circle you will see a spherical transverse wave move down the rope.
I hope that my entire audience has not fallen asleep completely. I also seriously hope nobody got seasick from all the moving animations in this article.
Now let’s move on to reality. An explosion or earthquake does not behave like a sine, a cosine, or any other regular wave. It is a bit shocking, really. In fact what it produces can be described as an instant, chaotic combination of waves of all different frequencies, slow and fast, large and small. It makes a mess. As the wave travels out, the high frequency components get dampened out. They suffer friction, loose energy and give up. At large distances, what remains is a much more regular affair which lacks the energetic chaos of youth and instead moves up and down with the assured slowness of experience. You can see the effect when winds blow into a channel of water. At the start, there are lots of small wavelets looking like a good start to seasickness. But soon it develops into a regular wave, inviting the viewer to a surfing experience.
We can see this behaviour after an earthquake. A seismograph near the earthquake dithers all over the place, certainly in no way sineful. But far away, the behaviour becomes much smoother. Here, as an example, is the measurement from the Alaskan earthquake of 2021, measured in far-away Iceland. Note the two different part of the waves. The first wave (P for primary) is irregular, while the stronger later wave (S for secondary) is much more sine-like.
The S-wave is the transverse wave, traveling a bit slower (and thus arriving a bit later) because of the continuous diversions which also shake out all the high frequency jitter. You can see a bit a beat in the signal, as waves of slightly frequency interfere, but otherwise it is well behaved. The P-wave is the longitudinal wave, traveling through rock as compression and decompression, just like a sound wave. It is faster but does not manage to shake off its irregular beginning and is just as messy as when it started.
For comparison, here is a seismograph near a large earthquake. This is not Alaska, but Christchurch, New Zealand, 2011. You can see it looks nothing like the long-distance wave. It carries the youthful chaos, before it shows the underlying sine wave.
Can we see all this hand-waving physics in the real world? Yes! Here is a wave pattern in water where regular waves pass in different directions, canceling each other out in some places, amplifying in other places. It gives a watery square grid pattern, as if inviting us to a game. (If you see this unexpectedly it might be wise to stay out of the water.)
For earthquakes, the P and S waves are discussed above. These travel through rock. But there are also surface waves which can do much of the damage close to the epicentre. They are slower than the P and S waves. There are two types, the Rayleigh waves which move up and down, and the Love waves which will throw you sideways. Such waves were reported from the Lisbon earthquake, where buildings were said to be waving back and forth.
It is very difficult to find good videos of this in real life. You need a stable camera with a fixed viewing angle. Somehow, people who record phone videos during an earthquake run all over the place and point chaotically at the chaos, while traffic cameras provide a fixed view but can’t stop shaking. But here are two examples, one of swimming pools during earthquakes and the other of a fairly stable webcam, which give an indication of how the surface moves. In the second example, note how the people are stumbling sideways, not up and down.
Gravity waves are sometimes seen in clouds. The movement is up and down, driven by a disagreement between gravity and air pressure and caused by sudden vertical motions (e.g. an eruption). (Ocean waves are also gravity waves.) Clouds can form during the ‘up’ part of the wave, and dissolve again in the ‘down’ part, so you get cloud lines delineating the wave, in a circular pattern around the explosion site.
Waves in liquids are of course well known. They require low viscosity, otherwise they damp out too quickly. Hawai’i is known for its low viscosity lava, and waves have been seen in it. Don’t expect oceanic waves! They are ripples – but ripples in beauty.
The final example is the already famous Hunga Tonga explosion of 2022, the VEI 5.8 which behaved like Krakatau 1883. The air pressure wave traveled around the world three times, the first time this happened in more than a century. Here is a video of its progress.
With that, the physics lecture is over and you may now wake up. If there is one bottom line, it is that waves happen everywhere. From starling murmurations to traffic jams, from swimming pools to clouds, they are there to be seen wherever something disturbs the world. It is there for us to see and hear.
And if you ever happen to find yourself in a large earthquake, please keep you phone stable, and directed along a long straight road. You’ll be forever remembered.
CARL & albert