I cannot for the life of me properly understand waves and energy in physics, no matter how many definitions and explanations I come across.
I can do calculations with all of these things, but I have trouble understanding what they represent in reality. Can I touch a wave? Is a wave a physical thing like an object, that moves up and down? Ditto for energy.
The definitions of these things are kinda unhelpful. Defining wave as “thing that transfers energy” doesn’t tell me what that *thing* is, for example; it just tells me something about the thing.
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> Is a wave a physical thing like an object, that moves up and down?
The definition is extremely vague because waves are a very broad concept. A wave is anything that satisfies the [wave equation](https://en.wikipedia.org/wiki/Wave_equation).
Pressure waves occur because adjacent particles push on each other, and when everything is pushing on each other the values of displacement (if we’re in a solid lattice) and pressure both satisfy the wave equation. So, if there is some unequal distribution of pressure in the substance, this unneveness will travel throughout it.
Surface waves occur because the surface of a fluid pulls down on adjacent portions, wanting to return to a flat surface. When a surface pulls on itself in this way, the height above the surface satisfies the wave equation, so an unequal distribution of heights will propagate across the surface.
And so on. Every form of wave may have a unique way of storing and transferring energy. Surface waves have energy stored in the velocity of fluid particles, and in gravitational potential. Pressure waves have energy stored in the velocity of particles, and in the electrical potential when the particles are squeezed together by a high pressure.
Some waves are even more abstract. Electromagnetic waves are waves in the electromagnetic field. Rather than a substance, this field is more like a capability that all of spacetime has to hold some kind of vector, and have adjacent vectors interact with each other. Quantum waves are similar, except instead of being a real vector that we can observe, quantum fields hold some kind of unobservable quantity, and we can only predict the consequences of that quantity having some set of values. But, just the same as matter waves, both of these satisfy the wave equation, and for both of them we have ways of calculating energy density, and situations in which that energy can be transferred from the wave to an object.
Perhaps something that might help simplify the relationship between waves and energy is the fact that, if a wave did not both contain energy and have a way for that energy to interact with us, we would never observe it. Transferring energy is the only way objects in the universe can interact with each other. Perhaps there are waves without any energy out there, and we simply can never interact with them. So, waves are really things that satisfy the wave equation, but the waves we care about are those that can store and transfer energy.
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