# Where does wave frequency come from?

I am trying to wrap my head around where do oscillations in electromagnetic waves come from. As an example if I would take a string of guitar and ring it, it would produce a certain sound based on the amount of vibrations per second. That amount of vibrations would be the sum of moves of string per amount of time, e.g there is one oscillation happening many times until string runs out of energy.

When I see the visible light it must be same thing something is vibrating and all the oscillations must the the sum of 'something' of one.
What is producing that one oscillation?

For low-frequency radiation, it's quite simple: there's some electronic circuit that works (simple case) analogous to a tuning fork, but instead of building up mechanical tension it charges a capacitor and instead of the inertia in the fork's arms it has a magnetic field in a solenoid. You can measure the voltage against time, count the oscillations in one second, and know your frequency in Hertz.

For visible light, this explanation doesn't quite work anymore, but still it's kind of sort of vibrations – on an atomic scale! These systems must be described in quantum states, and there's this thing that if a state has energy $E$ then you can assign it a frequency $\nu = E/h$, where $h$ is the Planck constant. This frequency can't be observed directly, but what you can observe is, for a quantum superposition of two states with different energy $E_1, E_2$, that the system kind of "wiggles" with a frequency $\Delta\nu = \tfrac{E_1 - E_2}{h}$. And that wiggling frequency is the frequency of light emmited by a transistion from state 1 to state 2.

(Of course this explanation does not quite reflect how quantum mechanics works, just a very rough picture.)

• So if I would want to get one 'wiggle' I would have to take E1 - E2 to be equal to planks constant. Are there such E1 and E2 known by any chance? – Matas Vaitkevicius Jul 29 '14 at 18:32
• No. You can't have "just one wiggle". Your concept that an oscillation is a sequence of separate cycles doesn't hold, certainly not on the quantum level. What you can create is a short pulse with only a few (strong) cycles – but the shorter you want it, the more complicated it gets: as Fourier transform tells us, to get a compact peak in time we need to combine a whole lot of frequencies! That's what ultrashort-pulse lasers use. – leftaroundabout Jul 29 '14 at 21:10

The thing which is "vibrating" is the electromagnetic field, namely its $\vec E$ and $\vec B$ vectors. The animations here show precisely this.

Of course, it's not that some particles vibrate in this case. The electromagnetic wave can exist without any matter at all — all it needs is the field, which is present everywhere.

But, if we have some charges around, they can be made to vibrate and produce the electromagnetic wave. After the wave is produced, the charges can be removed — the wave is a self-sustaining entity.

At the very beginning of electrodynamics there was a model of luminiferous aether, which assumed that there was some medium in which the electromagnetic waves propagate like mechanical waves. But this model had serious problems, which lead to development of special relativity theory.

## protected by Qmechanic♦Jun 28 '17 at 18:31

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