Wavelength
Distance over which a periodic wave's shape repeats; relates to frequency and speed and is central to optics, acoustics, and wave physics.
Overview
A wavelength is the spatial period of a repeating wave—the distance over which the wave's shape repeats itself. It is commonly denoted by the Greek letter lambda (λ). For a wave that travels at speed v and oscillates at frequency f, wavelength and frequency are inversely related by the simple relation λ = v / f. In many contexts the term applies to electromagnetic waves, sound waves, water waves, and even quantum wavefunctions.
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Key properties
Wavelength is distinct from amplitude (the height of oscillation) and from phase (the relative position within a cycle). Closely related quantities include the period (time for one cycle), the wavenumber k = 2π/λ, and the distinction between phase velocity and group velocity in dispersive media. In quantum contexts a particle's de Broglie wavelength connects momentum to wave behavior.
How waves are described
Many complex waveforms can be decomposed into simpler sinusoidal components. A pure sine wave is characterized by a single wavelength and frequency; more complicated shapes are formed by adding sine waves of different wavelengths and amplitudes. For an introduction to the elementary sinusoid see sine wave, to the general idea of waves see waves, and to the mathematical method that extracts these components see Fourier analysis.
Examples and scales
- Visible light has wavelengths roughly in the range of a few hundred nanometres, with violet shorter and red longer.
- Radio waves span metres to kilometres, while microwaves and infrared occupy intermediate ranges.
- Sound in air at everyday frequencies has wavelengths from millimetres to metres depending on pitch.
History and importance
The idea of wavelength emerged as scientists studied interference and diffraction: patterns that occur when wavefronts overlap reveal a characteristic spacing tied to wavelength. Understanding wavelength was crucial for the development of optics, electromagnetic theory, and later quantum mechanics. Practical technologies—telecommunications, spectroscopy, imaging, and acoustics—rely on controlling or measuring wavelength.
Distinctions and notable facts
Wavelength is a spatial measure and should not be confused with period, which is temporal. In materials where wave speed depends on frequency (dispersion), different spectral components travel at different speeds, so a wave packet's group velocity can differ from its phase velocity. Wavelength also sets the scale for phenomena such as diffraction and resolution: features much smaller than a wavelength are generally difficult to detect with wave-based probes.
Wavelength of sound waves
The human ear is sensitive to frequencies of at most about 16 hertz to 20 kHz (corresponding to a wavelength range of about 21 m to 17 mm at a sound propagation velocity in the medium air of 
= 343 m/s), although the ability to perceive higher frequencies generally decreases with age. Since the wavelength is proportional to the speed of sound propagation in the medium of propagation, a sound with a frequency of 16 hertz in water ( = 1484 m/s) has a wavelength of approximately 90 m. The auditory impression, the pitch, is given by the frequency, not by the wavelength in a medium outside the ear, because the sound propagation velocities of the media in the inner ear-and thus the wavelengths of a given sound occurring there-are independent of the media through which the sound reaches the eardrum. Certain animal species can also perceive sound waves with lower or higher frequencies, hence sound of other wavelength ranges.
Wavelength of electromagnetic radiation
→ Main article: Electromagnetic spectrum
Wavelengths of visible light: Colors
See also: Color
The human eye is sensitive in a wavelength range from about 380 nm (violet) to 780 nm (red). Bees also see shorter wavelength radiation (ultraviolet), but cannot perceive red light for it. Under optimal conditions, the limits of human perception can be 310 nm (UV) to 1100 nm (NIR).
Wavelength of electromagnetic waves in the medium
For the wavelength in a medium holds:
Where is the speed of light in vacuum, μ 
is the magnetic permeability and ε 
is the relative permittivity of the medium. When electromagnetic waves pass through a medium whose refractive index 
greater than 
, this reduces the wavelength and the speed of propagation. The frequency of the wave remains the same. The wavelength in the medium is
where λ 
is the wavelength of the electromagnetic wave in vacuum.
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AlegsaOnline.com Wavelength Leandro Alegsa
URL: https://en.alegsaonline.com/art/106925