How does the frequency of waves relate to their energy?

The relationship between the frequency of waves and their energy is fundamentally based on the principles of wave mechanics and quantum theory. Higher frequency waves have more energy because of the equation that describes the energy of a photon, which is given by E = hf, where E is energy, h is Planck's constant, and f is the frequency of the wave.

As the frequency increases, the energy of the wave correspondingly increases. This is particularly relevant for electromagnetic waves, such as visible light, ultraviolet light, and even X-rays; as you move from lower frequency waves like radio waves to higher frequency waves, the energy associated with these waves becomes greater. For instance, ultraviolet light has more energy than visible light due to its higher frequency, while X-rays have even higher energy due to their even greater frequencies.

Thus, the correct understanding is that waves with higher frequencies carry more energy, which aligns directly with the principles of wave behavior in physics. This relationship is crucial in various applications, including understanding how different types of radiation interact with matter, such as in heating, medical imaging, and telecommunications.