How is wavelength related to a wave's energy?

The energy of a wave is inversely proportional to its wavelength, meaning as the wavelength increases, the energy decreases.

In more detail, the relationship between a wave's energy and its wavelength is governed by the Planck-Einstein relation. This equation states that the energy (E) of a wave is equal to Planck's constant (h) multiplied by its frequency (f). The frequency of a wave is inversely proportional to its wavelength (λ), which is expressed in the equation f = c/λ, where c is the speed of light. Therefore, the energy of a wave can also be expressed as E = hc/λ.

This means that as the wavelength of a wave increases, its frequency decreases, resulting in a decrease in energy. Conversely, as the wavelength decreases, the frequency and therefore the energy increases. This relationship is particularly important in the field of quantum mechanics, where it is used to describe the properties of photons and other particles.

For example, consider light waves. Light with a short wavelength, such as blue or violet light, has a higher frequency and therefore more energy than light with a long wavelength, such as red or orange light. This is why ultraviolet light, which has an even shorter wavelength than visible light, has enough energy to cause sunburn.

Understanding the wave parameters is crucial for comprehending how wavelength and frequency contribute to a wave's energy. Furthermore, different types of waves possess unique characteristics that affect their energy. The concept of wavefronts and rays further illustrates the propagation of these energies in physical space.

In the context of sound waves, the energy is related to the amplitude rather than the wavelength. However, in electromagnetic waves, which include light, radio waves, X-rays and others, the energy is indeed inversely proportional to the wavelength. This principle is fundamental in various applications, from the design of antennas to the understanding of atomic spectra.

IB Physics Tutor Summary: The energy of a wave decreases as its wavelength increases, based on the Planck-Einstein relation. This formula shows energy is proportional to frequency but inversely proportional to wavelength. This concept is essential in quantum mechanics for understanding photon energies. In electromagnetic waves, such as light, shorter wavelengths mean higher energy, unlike sound waves where energy is linked to amplitude.