As wavelength decreases, what happens to the energy of a wave?

As the wavelength of a wave decreases, the energy of the wave increases. This relationship stems from the fundamental equation that relates wave energy to its frequency:

[ E = h f ]

where (E) is the energy of the wave, (h) is Planck's constant, and (f) is the frequency of the wave. The frequency of a wave is inversely proportional to its wavelength, as described by the equation:

[ c = f \lambda ]

where (c) is the speed of light, (f) is the frequency, and (\lambda) is the wavelength. When the wavelength decreases, the frequency increases. Since energy is directly proportional to frequency, as the frequency of the wave increases due to a decrease in wavelength, the energy also increases.

This principle applies to various types of waves, including electromagnetic waves. For instance, in the electromagnetic spectrum, gamma rays have shorter wavelengths and much higher energy compared to radio waves, which have longer wavelengths and lower energy. Thus, as wavelength decreases, the energy of the wave indeed increases.