Part 1 in the series can be found here: https://volcanocafe.wordpress.com/2014/06/06/earthquakes-or-wavy-gravy/
In the first installment I told a blatant lie, I thought someone would catch me, but alas not. The lie was put in on purpose so that I would have a point to start today’s wavy post with. In short, in the last installment 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. 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 in gas or fluid media. There are a couple of exceptions but we can leave those behind.
But in solid media there is another type of mechanical audio wave lurking in the shadows and it travels in something called a transverse wave. It is time to enter the seductress of wave physics, the cosine wave.
The sine and the cosine is in a way the same conundrum as the classical, “which came first, the hen or the egg?” Let us start with saying that the sine wave is a 2+1-dimensional wave and that the cosine is 3+1-dimensional.
The sine wave moves up and down (height) and forwards (distance), it also travels through time. This extra time dimension I added is just me being nitpicky, all macro-cosmal waves moves forward in time.
The cosine is a function as the wave spirals around in a drawn out circle, so you have height, width and distance (and time). But really, I can use words or I can give you this sexy little animation I found in Wikipedia. It will tell you everything you need to know.
Now someone is probably muttering that a sine wave and cosine wave are just sinusoids of different phases, or that the cosine leads the sine wave or even that the sine lags the cosine. This is of course true, but in the end the cosine has one astounding difference as it carries the sound of the earthquake. Fasten your seatbelts; this will be an eye-opener that you will remember every time you see the simple representations of an earthquake on a drumplot, because now you will understand better what really is going on.
Now that we have looked briefly on the cosine wave we are ready for the transverse wave. Now, remember that the cosine wave is a mechanical audio wave, and that the transverse wave is how the cosine propagates (moves around). But let us first take a refresher look at the creation and travel of the longitudinal sine wave through let us say Iceland.
As people set up new sciences they tend to want to differentiate themselves from the parent discipline. In physics it is a transverse wave, in Geologese it is a seismic S (secondary) wave. But basically it is the same shit with a different name.
The two most often occurring versions of transverse waves are the planar transverse wave (megathrusts 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 Emediately 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 think this will be enough for today. I just hope that my entire audience has not fallen asleep completely. Next time I will do my very best to envelope you all in the warm embrace of the third part that governs every waveform, the envelope. I seriously hope nobody got seasick from all the moving animations I used in this article.