Waves with higher frequencies possess shorter wavelengths. This relationship is rooted in the fundamental wave equation, which states that the speed of a wave is equal to its frequency multiplied by its wavelength. When the frequency increases, and if the wave speed remains constant, the wavelength must decrease to maintain this equation.
For example, consider electromagnetic waves: as the frequency of visible light transitions from red to violet, the wavelength decreases from approximately 700 nm to about 400 nm. This principle applies across all types of waves, including sound and water waves.
Shorter wavelengths are indicative of higher frequencies, which often correlate with greater energy. This is why waves such as gamma rays, which have very high frequencies, also have very short wavelengths and carry significant energy compared to lower-frequency waves like radio waves. Understanding this relationship between frequency and wavelength is crucial in various applications within physics, such as telecommunications, sound engineering, and optics.