wavelength

Wavelength is the spatial period of a wave—the distance over which the wave's shape repeats. It is usually denoted by the Greek letter lambda (λ). Wavelength applies to all waves, including electromagnetic radiation, sound, and matter waves in quantum mechanics. For a traveling wave with speed v and frequency f, the wavelength is λ = v / f. In a vacuum, electromagnetic waves propagate at the speed of light c, so λ = c / f. In a medium, the wave speed is v = c / n, giving λ = v / f.

For light, wavelength helps determine color in the visible range (roughly 380 to 750 nanometers). The electromagnetic spectrum spans radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, each with characteristic wavelength ranges. The energy of a photon is E = h f = h c / λ, so longer wavelengths correspond to lower photon energy.

Measuring wavelength involves interference, diffraction, or spectroscopy. Interferometers detect phase differences to infer λ; gratings and prisms disperse light to identify wavelengths. Wavelength is a practical parameter in imaging, communications, and astronomical observations.

In quantum theory, matter can exhibit wave-like behavior with a wavelength given by λ = h / p, where p is the particle's momentum (the de Broglie relation). This connects wavelength to momentum and energy and underpins many quantum phenomena.