Wavelengths

Wavelength is the spatial period of a repeating waveform, the distance over which the wave’s shape repeats. It is a fundamental property of waves—electromagnetic, acoustic, or mechanical—and depends on the velocity of the wave in its medium. For waves in vacuum, wavelength λ is related to frequency f by λ = c/f, where c is the speed of light. In a medium, where the wave travels at speed v, the relation is λ = v/f. In optics, wavelengths are commonly expressed in meters, nanometers, or angstroms; visible light occupies roughly 380 to 750 nanometers.

In electromagnetic theory, the speed in a medium is c/n, where n is the refractive index, so the wavelength becomes λ = λ0/n, with λ0 the vacuum wavelength. Dispersion occurs when n varies with wavelength, causing different wavelengths to propagate at different speeds and changing pulse shapes. The wavenumber k = 2π/λ is frequently used in wave equations.

The concept underpins many applications, including spectroscopy, interferometry, and imaging, where specific wavelengths are selected using filters, prisms, or diffraction gratings. In acoustics and other fields, wavelength relates to frequency and speed via v = fλ, enabling the characterization of sound and water waves as they reflect, refract, or diffract.