Superposition's effect on frequency?

[Mzzed]

Imagine two electromagnetic waves are traveling in opposing directions such that they eventually meet, overlap, and continue traveling as usual after the superposition/overlapping event. Just before they overlap there is some superposition effect taking place but not enough to fully merge the two waves. They are at this point only partially merged and there are two peaks fairly close together forming what looks like a higher frequency pair of waves, would the resulting peaks being closer together affect the apparent frequency of the overall wave? I am also interested in the answer to this where both waves are traveling in the same direction but in the same semi-merged state with two peaks close together.

The event I am trying to describe is at time t2 and t4 in the image bellow

 

[Dale]

The Fourier transform is linear also, so it also obeys the principle of superposition. The frequency content of the combined signal is just the complex sum of the frequency contents of the individual signals.

 

[Mzzed]

The Fourier transform is linear also, so it also obeys the principle of superposition. The frequency content of the combined signal is just the complex sum of the frequency contents of the individual signals.

Would this enable non-ionizing radiation to ionize materials where ever these higher frequencies are formed?

 

[Dale]

No higher frequencies are formed. The Fourier transform just adds together, it does not shift.

 

[DrClaude]

Would this enable non-ionizing radiation to ionize materials where ever these higher frequencies are formed?

Multi-photon processes are possible, where a transition between two quantum levels of energy difference $\Delta E = \hbar \omega$ is achieved using two photons of lower frequencies $\omega_1 + \omega_2 = \omega$. But for that to happen at a significant rate, high photon densities are required, the kind you only get with powerful lasers.

 

[Dale]

Multi-photon processes are possible, where a transition between two quantum levels of energy difference $\Delta E = \hbar \omega$ is achieved using two photons of lower frequencies $\omega_1 + \omega_2 = \omega$. But for that to happen at a significant rate, high photon densities are required, the kind you only get with powerful lasers.

And that is a nonlinear process where superposition does not apply. It does not happen from superposition, but from violations of superposition.

 

[Mzzed]

Ah thankyou both, definitely clears this up for me!