[DISCLAIMER: i am NOT a physics expert, and this article does NOT aim for scientific rigor. there are likely many inaccuracies, as i am merely an amateur. please do not throw tomatoes at me]
yesterday, i went to the forest near where i live. if you go to the more "accessible" area -i'm not sure if that's the right term, but it's the one that comes to mind right now- there's a beautiful spring that actually gets quite a few visitors. however, as you venture deeper into the woods, the level of human presence drops off sharply. not completely, since the path is clearly defined and there's even a section with a rope, but the average person wouldn't go that far unless they specifically wanted to scramble over rocks and moss, it's a somewhat "dangerous" trail. that said, you're probably wondering: what does this have to do with waves? don't get ahead of yourself, all in good time.
after walking for a while (if you could even call it a walk), i spotted a small... pond? small lake? puddle? i really don't know what to call it. it was a fairly large hole, big enough for a person to lie stretched out flat, so it must have been a bit over a meter and seventy centimeters long. the opening was quite narrow, just wide enough for two people to sit side-by-side, but it widened as you went in. ultimately, it was deep enough to submerge half one's body. how deep is that? i don't know. i've never measured my torso. the hole was filled with water cascading down from the stream.
now that i've covered the preamble, let's get to the meat of the matter, the interesting, substantial part. i sat on one of the rocks at the entrance i mentioned earlier, dipped my feet in, and let the water wash over me up to my knee. that was when i picked up a small twig and started playing with it. i noticed that with every tap of the stick against the water's surface, every movement of my legs, and most clearly every drop falling from the stick itself, tiny ripples formed around the point of disturbance. as a former (and current) stem student, i already had a rough idea of how these waves work, but the subject still fascinates me and could easily become a bottomless rabbit hole, the concepts are so complex that i could spend a whole year researching them and still not be finished.
according to Wikipedia, the definition of a wave is as follows:
a wave (from the latin unda) consists of the propagation of a fluctuation or disturbance in a property of space—such as density, pressure, an electric field, or a magnetic field—involving the transport of energy without the transport of matter.
basically, what travels isn't a "thing". take sound, for example. it isn't the air or some "sonic" particle moving from the source to our ears, but rather the movement itself. a good illustration might be the "wave" people do in stadium stands: the movement is what passes from one person to the next, each individual simply stands up and sits back down. what propagates is that act of standing and sitting, it isn't a person actually moving along the stands. does that make sense? i hope so. mind you, not all waves require a medium to propagate (like air for sound, or the crowd itself for the stadium wave) ,electromagnetic waves -including visible light- can travel through the vacuum. we'll leave the details of exactly how that happens for another post, if i feel like it.
to describe a wave in basic terms, we use the wave equation (how many times have i said "waves" already? let's make it a drinking game)
in which
y(x, t): displacement of the wave at position x and time t. the wave function itself
t: time
x: position in space
v: propagation speed of the wave
one of the simplest wave functions is the sinusoidal wave
A: amplitude
k: angular wave number,
λ: wavelength,
ω: angular frequency,
f: frequency
ϕ: phase constant
waves do fun things, too. as i mentioned earlier when talking about my experience at the forest pond, ripples formed whenever i moved my legs or when droplets fell from the branch. if the ripples were close to one another, they would overlap creating a larger wave for a brief moment. the amplitude increases at that point because, by chance, both waves had their crests there. had one been a crest and the other a trough, they most likely would have cancelled each other out, assuming their amplitudes were equal.
one type of wave i find particularly hard to understand is the longitudinal wave. i understand the ones formed with a spring and the concept itself, but generally speaking, i find it difficult to visualize them. the example of sound i mentioned earlier applies here, too; i know sound waves are longitudinal and the concept makes sense, but i don't quite fully comprehend the mechanics of the wave itself. once it has propagated through a specific point in space, does the medium move back? i don't mean the medium itself (like air) traveling along the path of propagation, but rather a local oscillation. because theoretically, that's what should happen, right? each air particle moves forward, and after colliding with the next molecule, it returns to its original position. theoretically, it makes perfect sense, but perhaps it's my macroscopic brain struggling to picture that happening in real life. this is what i get for being human i guess, haha.
one type of wave i discovered while doing research is the love wave. i was already aware of their existence (kind of), but i had no idea what they were called. these seismic waves are transverse, but instead of following a vertical direction (commonly the Y-axis), they follow the "Z-axis", the axis of depth. i put that in quotation marks because it is somewhat arbitrary; however, if we use the convention where the Y-axis represents height and the X-axis represents the direction of wave propagation, then yes, the wave is transverse and follows the Z-axis, as it must be perpendicular to the direction of propagation yet parallel to the ground surface. furthermore, the amplitude decreases vertically. i think this is easier to understand with an image.
edit: aug 20 - i just realized that the axis are completely different from what i described. but it should make sense anyway
there are so many things in the world dictated by waves. right now, you're reading this via your internet connection: waves. every sound we hear is waves, everything we see is waves, it's all waves. Waves, waves, waves. i don't know. things like this leave me thinking for a long time, then i start looking into it and end up spending an entire afternoon and evening reading about a specific topic (in fact, that's exactly what i did for this post, i've spent more time reading about waves than actually writing this).