Superposition's effect on frequency?

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Discussion Overview

The discussion revolves around the effects of superposition on the frequency of electromagnetic waves, particularly when two waves overlap partially. Participants explore the implications of this superposition on the perceived frequency and the potential for non-ionizing radiation to ionize materials under certain conditions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes a scenario where two electromagnetic waves partially merge, questioning whether the proximity of their peaks would affect the overall frequency of the resulting wave.
  • Another participant states that the Fourier transform is linear and adheres to the principle of superposition, suggesting that the frequency content of the combined signal is a complex sum of the individual signals' frequency contents.
  • A subsequent post reiterates the linearity of the Fourier transform and questions whether this could allow non-ionizing radiation to ionize materials due to the formation of higher frequencies.
  • Another participant counters that no higher frequencies are formed through superposition, emphasizing that the Fourier transform simply adds frequencies without shifting them.
  • Multi-photon processes are introduced as a mechanism where transitions between quantum energy levels can occur using two lower frequency photons, but this requires high photon densities typically found in powerful lasers.
  • It is noted that such multi-photon processes are nonlinear and do not arise from superposition, but rather from violations of superposition.
  • A later reply expresses gratitude for the clarification provided by the participants, indicating a resolution of confusion for that individual.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the effects of superposition on frequency, particularly whether higher frequencies can be formed. Some assert that superposition does not lead to frequency shifts, while others explore the implications of multi-photon processes, indicating that the discussion remains unresolved on certain points.

Contextual Notes

The discussion includes assumptions about the nature of wave interactions and the conditions under which multi-photon processes occur, which may not be fully explored or defined.

Mzzed
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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
CNX_UPhysics_16_05_InterSup1.jpg
 
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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.
 
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Dale said:
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?
 
No higher frequencies are formed. The Fourier transform just adds together, it does not shift.
 
Mzzed said:
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.
 
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DrClaude said:
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.
 
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Ah thankyou both, definitely clears this up for me!
 

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