Higher frequency => higher energy

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High-frequency waves have higher energy because the energy of each photon is directly proportional to its frequency, as described by the equation E=hf, where h is Planck's constant. While the energy of a wave is also related to its amplitude, which correlates with the number of photons, the frequency itself plays a crucial role in determining energy levels. Higher frequency oscillations require a stronger restoring force, indicating that more energy is needed to achieve the same displacement. Additionally, a higher frequency results in more peaks and troughs in the wave, contributing to increased energy. Understanding these principles clarifies the relationship between frequency and energy in waves.
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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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