Higher frequency => higher energy

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Discussion Overview

The discussion revolves around the relationship between wave frequency and energy, specifically focusing on electromagnetic (EM) waves. Participants explore intuitive explanations and mathematical principles related to this concept.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for an explanation of why high frequency waves contain higher energy.
  • Another participant explains that for EM waves, the energy of each photon is given by the equation E=hf, where h is Planck's constant and f is the frequency, suggesting that the statement about waves "containing" energy is not entirely accurate.
  • A different participant provides two intuitive answers: one relating to the stronger restoring force required for higher frequency oscillations in a simple harmonic oscillator, and another stating that higher frequency results in more peaks and troughs, implying more energy is involved.
  • This participant acknowledges that their intuitive answers are imprecise and suggests that the mathematical description is clearer.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the relationship between frequency and energy, with some agreeing on the photon energy equation while others provide alternative intuitive explanations. The discussion does not reach a consensus on the best way to articulate the concept.

Contextual Notes

Some explanations provided are noted as imprecise or hand-wavy, indicating limitations in the clarity of the intuitive descriptions compared to mathematical formulations.

LLT71
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can someone explain why high frequency waves contain higher energy?

thanks!
 
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If these are EM waves we are talking about, then each photon has energy equal to hf where h is Planck's constant and f is the frequency of the wave. To say that high frequency waves "contain" higher energy is not quite correct. The energy of a wave is proportional to the square of the amplitude, which is related to the number of photons. So certainly it is correct to say that a photon of higher frequency has higher energy.
 
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LLT71 said:
can someone explain why high frequency waves contain higher energy?
One intuitive answer:
All else being the same, it takes a stronger restoring force to produce a higher frequency oscillation - the easiest way to see this is to play around with the equation for a simple harmonic oscillator. A stronger restoring force means more energy is needed to produce the same displacement.

Another intuitive answer: The energy of a wave is in whatever pushes the peaks up and the troughs down. A higher frequency means more peaks and troughs, hence more energy.

Both of these answers are imprecise and hand-wavy descriptions of something that is clear and precise in the math.
 
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thank you guys!
 

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