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The energy of a wave increases as its frequency increases, according to the Planck-Einstein relation.

In more detail, the energy of a wave is directly proportional to its frequency. This relationship is described by the Planck-Einstein relation, which states that the energy (E) of a wave is equal to its frequency (f) multiplied by Planck's constant (h). In mathematical terms, this is expressed as E=hf.

Planck's constant is a fundamental constant of nature that has a value of approximately 6.63 x 10^-34 joule-seconds. This means that even a small increase in frequency can result in a significant increase in energy, due to the multiplication by Planck's constant.

This relationship between energy and frequency is particularly important in the field of quantum mechanics, where it is used to describe the behaviour of particles at the atomic and subatomic level. For example, it explains why higher-frequency light waves, such as ultraviolet rays, can cause more damage to biological tissue than lower-frequency waves, such as visible light. This is because the higher-frequency waves carry more energy, which can disrupt the bonds between atoms and molecules.

In addition, the relationship between energy and frequency also has implications for the study of electromagnetic waves. For instance, radio waves have lower frequencies and therefore lower energies, while gamma rays have very high frequencies and correspondingly high energies.

In conclusion, understanding the relationship between a wave's frequency and its energy is crucial in many areas of physics. It not only helps us understand the behaviour of waves and particles at a fundamental level, but also has practical applications in fields ranging from medicine to telecommunications.

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