Higher frequency => higher energy

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SUMMARY

High frequency electromagnetic (EM) waves contain higher energy due to the relationship defined by the equation E = hf, where E is energy, h is Planck's constant, and f is frequency. While the energy of a wave is also proportional to the square of its amplitude, higher frequency photons inherently possess greater energy. Additionally, producing higher frequency oscillations requires a stronger restoring force, which necessitates more energy for the same displacement. Thus, both the mathematical relationship and physical intuition support the conclusion that higher frequency correlates with higher energy.

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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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