The up/down thing is just a visual. Really what’s happening is the constituent particles of whatever medium supports the wave are getting squished together/spread apart. So if someone shakes a rope the waves look like a line, but only because the rope is itself linear. if instead you imagine a rock dunking into a pond, the ripples that spread out around it are in 2 dimensions on the pond surface, but a hemisphere underwater (you just can’t see that). if a speaker is emitting sound or a light is shining, the waves radiate out from it in every direction until something stops them. And the waves just consist of looser/denser packing of the stuff (air, water, electrons, whatever is there). Like a stop-n-go traffic jam.
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