I see lots of drawings illustrating amplitude, frequency, etc using a sine wave to represent an EM wave, but why are they drawn like this? What do the crests and troughs mean/what values do they represent? And what do these waves look like in real life?
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The axis of the sine wave is the direction of the wave (actually it spreads in a sphere but if you transmit a wave between point A and point B, you only need to consider this line). Along that axis, the wave represents the intensity of electric and magnetic field.
Actual electromagnetic wave is pulsating in a “high electric field/low magnetic field – high magnetic field/low electric field” fashion with fields quickly changing polarities and intensities. But it’s an actual sine wave: electric field intensity can be described as a sin function (of distance or time) while magnetic field intensity will be cos function for the same parameter.
The electric and magnetic field are at 90 degrees to each other and 90 degrees to both of them is the direction of propagation (the poynting vector, which is also the energy flux). Think of the edge of a cube, you have three edges at 90 degrees to one another.
Now the amplitude of the wave is the maximum strength of the electric and magnetic fields. The frequency is how fast it goes through that cyclic change.
To answer *How does it actually look*? It’s just a bunch of photons traveling through space having that variation described – the photon travels in a straight line (if it doesn’t get affected in it’s path).
So when drawings show the amplitude and frequency, they’re showing the electric and magnetic field strength (amplitude) varying at a certain cyclic rate (frequency).
But humans can’t see radio waves because their wavelengths are about 1mm to up to 10,000 km so they have no *color* for us to see them.
Radio waves are part of the electromagnetic spectrum, and we can only see a part of this spectrum. The part we can see is called visible light – which is 700 nm (red) to 400 nm (violet) wavelengths.
Imagine fluid flowing around in some large body of water – you’re going to have internal currents going in all different directions. At every point in space, attach an arrow. This arrow points in the direction the water is flowing, and the length of the arrow tells you how fast it’s flowing.
These arrows form a vector field. Every point in space points in some direction with some intensity.
Electromagnetic waves are also described by vector fields, except nothing is flowing. Space itself can point in some direction with some intensity. In fact, it can point in an electric way (the electric field) and in a magnetic way (the magnetic field) at the same time.
When people draw those diagrams, they’re taking an EM wave which has some extent in space (like a sound wave – it spreads out in all directions), and look at the electric and magnetic fields along a single line of travel. The waviness is actually depicting where the field is pointing at every step of this line. This has direct physical consequences, if you were able to walk along an electromagnetic field without it moving, and carry a compass along the line that was being graphed out, you would see the compass point in one direction, then the other direction, then back, matching up with the graph (assuming this EM wave was stronger than the Earth’s magnetic field). Likewise with the electric field, if you had an electric field sensor – it would point back and forth, but perpendicular to the magnetic direction.
You know how you can take a cup with two strings and pull them tight to talk to someone? What’s actually happening there is the waves, generated by your voice, hit the inside of the cup (to make it vibrate) then vibrating the string and doing the same to your friend’s cup.
The waves themselves don’t actually have to be smooth and wavy; we have ones that look like triangles, squares, circles, squiggles, and even random static. This is one way of creating different sounds.
However, the shape *does* have to have some shape to it, and here’s why.
In the cup-and-string example, the molecules in the cup/string are getting shoved back and forth to generate a sound. Our ears capture this motion and interpret it as sound.
If we had no movement (and our shape would be a straight line), we have no vibration, and thus no sound.
Here is how waves happen:
1. Move something away from where it wants to be
2. Let go, and the thing goes back to where it wants to be
3. The thing overshoots, and now it’s where it doesn’t want to be again, only this time it’s on the opposite side.
4. When it goes too far it eventually stops, comes back, and oversoots again
5. Rrepeat over and over again.
Note that the thing, whatever it is, doesn’t snap back instantaneously. It picks up speed, it’s moving at its fastest when it crosses the centre line (where it wants to be) and then once it overshoots it starts to slow down. Eventually it stops, just for an instant, then as it starts coming back it picks up speed again.
This thing could be a guitar string. Or a child’s swing in a park. Or an electrical field. As long as we have a force which is trying to return the thing to its home position.
Now what we want to do is see the shape of this movement. So I want you to imagine you have a roll of paper like one from a cash register, and a marker pen. And imagine you’re watching a video of a kids’ swing. You’re going to step through the video frame by frame. On the tape you’re going to put a dot to show the height of the swing above ground. And after every frame you’re going to advance the paper roll a little bit.
Those dots will form the wave drawing that you’re asking about. The motion of something moving back and forth like we described, if you also move it through space, will form a wave like that. Guitar string, swing, electrical field. Doesn’t matter.
The force which makes a guitar string return to the centre is tension in the string. The force which makes the swing return to the bottom is gravity. (I’m using the word force informally here.) When we create an imbalance in an electrical field it wants to retun to its rest state. But what makes it overshoot? What makes it springy?
When the electrical field is busily returning to its rest state, tgat has a sideways effect of creating an imbalance in the magnetic field, which wants to get back to *its* rest state. And when the magnetic field is busily returning to its rest state, that creates a new imbalance in the electrical field. And so on, and so on.
The strength of the electrical field grows and reverses and shrinks and grows and reverses and shrinks, with the same pattern as the guitar string or the swing. That very same wave pattern.
And that is why we draw them as we do.
The waves are mathematical model. They don’t exist in real life for us to “see”. They are also known to be inaccurate, so they can’t even represent a real physical entity.
So what does the model look like? You have a EM field, which is a assignment of a pair of vectors to each point, at each instance in time (so when time change the vectors change).
A pair of vector is difficult to draw, so what happen is that they take just 1 numerical value out of it, such as by projecting 1 vector on an axis. This gives you the vertical axis.
For the horizontal axis, it’s either distance or time. If it’s distance, you’re taking a snapshot at 1 instance in time, and look at all points along an axis in the direction the wave is moving. If it’s time, you’re fixing a single point and look at how the vectors at that point change over time.
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