The energy of a wave increases with its frequency, as described by the Planck-Einstein relation.

Specifically, the energy ($E$) of a wave is directly proportional to its frequency ($f$). This relationship is mathematically defined by the Planck-Einstein equation:

where $h$ represents Planck’s constant. This fundamental constant of nature has an approximate value of $6.63 \times 10^{-34}$ joule-seconds. Consequently, even a small increase in frequency can lead to a substantial increase in energy due to the multiplication by Planck’s constant.

This energy-frequency relationship is particularly significant in the realm of quantum mechanics, where it is utilized to explain the behavior of particles at atomic and subatomic scales. For instance, it elucidates why higher-frequency light waves, such as ultraviolet rays, can inflict more damage on biological tissues compared to lower-frequency waves like visible light. The reason is that higher-frequency waves carry more energy, which can disrupt atomic and molecular bonds.

Furthermore, this relationship has important implications for the study of electromagnetic waves. For example, radio waves, with their lower frequencies, correspond to lower energy levels, while gamma rays, which possess very high frequencies, are associated with significantly higher energies.

In summary, understanding the connection between a wave’s frequency and its energy is essential across various fields of physics. This knowledge not only deepens our comprehension of wave and particle dynamics at a fundamental level but also has practical applications in diverse areas, including medicine and telecommunications.