The energy of a wave can be determined using the formula

where $E$ represents the energy, $h$ is Planck’s constant, and $f$ is the frequency of the wave.

To elaborate, the energy of a wave is directly proportional to its frequency. This relationship is captured in the equation $E = hf$, where $E$ denotes the energy of the wave, $h$ (approximately $6.63 \times 10^{-34}$ Joule seconds) is Planck’s constant, and $f$ indicates the frequency measured in Hertz (Hz). This formula originates from quantum theory, which posits that light and all other forms of electromagnetic radiation can be modeled as discrete packets of energy called ‘quanta’, each possessing energy defined by $hf$.

To calculate the energy of a wave, the first step is to determine its frequency. The frequency of a wave is defined as the number of complete cycles that pass a specific point in a given time interval. It is typically measured in Hertz, which corresponds to cycles per second. Once the frequency is known, you can substitute it into the formula alongside Planck’s constant to compute the energy.

It is important to highlight that this formula is applicable to all types of electromagnetic radiation, not just visible light. This includes radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays. Each of these radiation types has a distinct frequency, and consequently, a different energy level. For instance, gamma rays possess very high frequencies and, as a result, exhibit very high energy, whereas radio waves have low frequencies and correspondingly low energy.

In summary, the energy of a wave can be calculated using the equation

This formula is a fundamental tenet of quantum mechanics and is essential for understanding the behavior of light and various forms of electromagnetic radiation.