Wavelength

The wavelength λ (Greek: lambda) of a periodic wave is the smallest distance between two points of the same phase. Two points have the same phase if they have the same displacement (elongation) and the same direction of motion in time. The wavelength is the spatial analogue of the periodic time.

In general

where the phase velocity and is the frequency of the wave.

However, for a given frequency, phase velocity and wavelength depend on the propagation medium and the geometry of the wave. If necessary, one speaks of vacuum wavelength or free-space wavelength to differentiate, if one does not mean the wave in the medium or the wave in a waveguide.

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

Wavelengths of visible light: Colors

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.

Overview of electromagnetic waves with the visible spectrum in detail