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Wavelength
 
 
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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, wavelength is the distance between repeating units of a propagating wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 of a given frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
. It is commonly designated by the Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
 letter
Letter (alphabet)

A letter is an element in an alphabetic system of writing, such as the Greek alphabet and its descendants. Each letter in the written language is usually associated with one phoneme in the spoken form of the language....
 lambda
Lambda

Lambda is the 11th letter of the Greek alphabet. In the system of Greek numerals it has a value of 30. It was derived from the Phoenician alphabet Lamed ....
. Examples of wave-like phenomena are light
Light

Light, or visible light, is electromagnetic radiation of a wavelength that is Visible spectrum to the human eye , or up to 380?750 nm. In the broader field of physics, light is sometimes used to refer to electromagnetic radiation of all wavelengths, whether visible or not....
, water waves, and sound waves. The wavelength is related to the frequency by the formula: wavelength = wave speed / frequency. Wavelength is therefore inversely proportional to frequency.






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Wavelength
In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, wavelength is the distance between repeating units of a propagating wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 of a given frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
. It is commonly designated by the Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
 letter
Letter (alphabet)

A letter is an element in an alphabetic system of writing, such as the Greek alphabet and its descendants. Each letter in the written language is usually associated with one phoneme in the spoken form of the language....
 lambda
Lambda

Lambda is the 11th letter of the Greek alphabet. In the system of Greek numerals it has a value of 30. It was derived from the Phoenician alphabet Lamed ....
. Examples of wave-like phenomena are light
Light

Light, or visible light, is electromagnetic radiation of a wavelength that is Visible spectrum to the human eye , or up to 380?750 nm. In the broader field of physics, light is sometimes used to refer to electromagnetic radiation of all wavelengths, whether visible or not....
, water waves, and sound waves. The wavelength is related to the frequency by the formula: wavelength = wave speed / frequency. Wavelength is therefore inversely proportional to frequency. Waves with higher frequencies have shorter wavelengths. Lower frequencies have longer wavelengths, assuming the speed of the wave is the same.

In a wave, properties vary with position. For example, in a sound
Sound

Sound is vibration transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a threshold of hearing to be heard, or the sensation stimulated in organs of hearing by such vibrations....
 wave the air pressure
Sound pressure

Sound pressure is the local pressure deviation from the ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water....
 oscillates, while in light
Light

Light, or visible light, is electromagnetic radiation of a wavelength that is Visible spectrum to the human eye , or up to 380?750 nm. In the broader field of physics, light is sometimes used to refer to electromagnetic radiation of all wavelengths, whether visible or not....
 and other electromagnetic radiation
Electromagnetic radiation

Electromagnetic radiation takes the form of wave propagation waves in a vacuum or in matter. EM radiation has an electric field and magnetic field component which oscillate in phase perpendicular to each other and to the direction of energy Wave propagation....
 the strength of the electric
Electric field

In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field ....
 and the magnetic field
Magnetic field

A magnetism field is a vector field which can exert a magnetic force on moving electric charges and on magnetic dipoles . When placed in a magnetic field, magnetic dipoles tend to align their axes parallel to the magnetic field....
 vary.

Visible light ranges from deep red
Red

Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 625?740 Nanometer....
, roughly 700 nm
Nanometre

A nanometre is a Units of measurement of length in the metric system, equal to one billionth of a metre .It is one of the more often used units for very small lengths, and equals ten ?ngstr?m, an internationally recognized non-International System of Units of length....
, to violet
Violet (color)

As the name of a color, violet is used in two senses: first, referring to the color of light at the short-wavelength end of the optical spectrum, approximately 380?420 nanometre when indigo is recognized, or more commonly 380?450 nm ....
, roughly 400 nm (430–750 THz). For other examples, see electromagnetic spectrum
Electromagnetic spectrum

The electromagnetic spectrum is the range of all possible electromagnetic radiation frequencies. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation from that particular object....
. The wavelengths of sound frequencies audible to the human ear (20 Hz
Hertz

The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
–20 kHz) are between approximately 17 m
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
 and 17 mm
Millimetre

The millimetre is a Units of measurement of length in the metric system, equal to one thousandth of a metre, which is the current International System of Units SI base unit of length....
, respectively, assuming a typical speed of sound
Speed of sound

Sound is a vibration that travels through an elasticity medium as a wave. The speed of sound describes how much distance such a wave travels in a certain amount of time....
 of about 343 m/s; the wavelengths in audible sound are much longer than those in visible light.

Relationship with frequency


Wavelength ? is determined using the formula

where v is the phase speed of the wave and f is its frequency. In the case of electromagnetic radiation
Electromagnetic radiation

Electromagnetic radiation takes the form of wave propagation waves in a vacuum or in matter. EM radiation has an electric field and magnetic field component which oscillate in phase perpendicular to each other and to the direction of energy Wave propagation....
, such as light, in a vacuum, this speed is the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
, 299,792,458 m/s or about 3×108
Scientific notation

Scientific notation, also known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation....
 m/s. For sound waves in air, this is the speed of sound
Speed of sound

Sound is a vibration that travels through an elasticity medium as a wave. The speed of sound describes how much distance such a wave travels in a certain amount of time....
, 343 m/s (1238 km/h) in air at room temperature and atmospheric pressure
Standard conditions for temperature and pressure

In physical sciences, standard conditions for temperature and pressure are standard sets of conditions for experimental measurements, to allow comparisons to be made between different sets of data....
. Usually, SI
Si

Si, si, or SI may refer to :...
 units are used, where the wavelength is expressed in metre
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
s, the frequency in hertz
Hertz

The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
, and the propagation speed is in metres per second
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
.

For example, the wavelength for a 100 MHz electromagnetic (radio) wave is about: 3×108 m/s divided by 100×106 Hz = 3 metres. Electronic engineers often use a shortcut formula: wavelength ? in metres = 300 Mm
Megametre

A megametre is a Units of measurement of length in the metric system, equal to one million metres, the International System of Units SI base unit of length, hence to 1,000 Kilometre or approximately 621.37 miles....
/s divided by the frequency in MHz, to avoid counting the (many) zero digits in the decimal
Decimal representation

A decimal representation of a non-negative real number r is an expression of the formwhere a0 is a nonnegative integer, and a1,...
 or scientific notation
Scientific notation

Scientific notation, also known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation....
s.

It should be noted that for many wave phenomena, wavelength is not the distance that particles travel during a period. For instance, in acoustics
Acoustics

Acoustics is the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician....
 and water waves, the particle displacements during a period are only a small fraction of the wavelength, apart from extreme conditions like breaking wave
Breaking wave

In physics, a breaking wave is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be dissipated....
s and shock wave
Shock wave

A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field....
s.

It should also be noted that frequency and wavelength can change independently, but only when the speed of the wave changes. For example, when light enters another medium, its speed and wavelength change while its frequency does not (cf. refraction
Refraction

Refraction is the change in direction of a wave due to a change in its speed. This is most commonly observed when a wave passes from one optical medium to another....
).

In non-vacuum media


The speed of light in most media is lower than in vacuum, which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum. The wavelength in the medium is

where ?0 is the wavelength in vacuum, and n is the refractive index
Refractive index

The refractive index of a medium is a measure for how much the speed of light is reduced inside the medium. For example, typical soda-lime glass has a refractive index of 1.5, which means that in glass, light travels at times the speed of light in a vacuum....
 of the medium. When wavelengths of electromagnetic radiation are quoted, the vacuum wavelength is usually intended unless the wavelength is specifically identified as the wavelength in the medium. In acoustics, where a medium is essential for the waves to exist, the wavelength in the medium is always the value given. Then the refractive index depends on the mean properties of the medium, for instance the mean pressure or changes in the material composition.

Subwavelength


The term subwavelength is used to describe an object having one or more dimensions smaller than the length of the wave with which the object interacts. For example, the term subwavelength-diameter optical fibre
Subwavelength-diameter optical fibre

Subwavelength-diameter optical fibre is an optical fibre which diameter is less than the wavelength of the light being propagated through the fibre....
 means an optical fibre whose diameter is less than the wavelength of light propagating through it.

A subwavelength particle is a particle smaller than the wavelength of light with which it interacts (see Rayleigh scattering
Rayleigh scattering

Rayleigh scattering is the elastic scattering of light or other electromagnetism radiation by particles much smaller than the wavelength of the light....
). Subwavelength aperture
Aperture

In optics, an aperture is a hole or an opening through which light is admitted. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of ray that come to a focus in the ....
s are holes smaller than the wavelength of light propagating through them.

Subwavelength may also refer to a phenomenon involving subwavelength objects; for example, subwavelength imaging
Subwavelength imaging

Subwavelength imaging is a unique imaging technique which allows visualization of features on the viewed object which are smaller than the wavelength of the photons in use....
.

De Broglie wavelength of particles


Louis de Broglie postulated that all particles with momentum
Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section Momentum#Modern definitions of momentum on this page....
 have a wavelength

where h is Planck's constant, and p is the momentum
Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section Momentum#Modern definitions of momentum on this page....
 of the particle. This hypothesis was at the basis of quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
. Nowadays, this wavelength is called the de Broglie wavelength. For example, the electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
s in a CRT
Cathode ray tube

The cathode ray tube is a vacuum tube containing an electron gun and a fluorescent screen, with internal or external means to accelerate and deflect the electron beam, used to create images in the form of light emitted from the fluorescent screen....
 display have a De Broglie wavelength of about 10–13 m.

See also


  • Amplitude
    Amplitude

    Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
  • Angular frequency
    Angular frequency

    In physics , angular frequency ? is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity....
  • Frequency
    Frequency

    Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
  • Fraunhofer lines
    Fraunhofer lines

    In physics and optics, the Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer . The lines were originally observed as dark features in the optical spectrum of the Sun....
    , spectral lines traditionally used as standard optical wavelength references
  • Periodic function
    Periodic function

    In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π....
  • Wave vector
    Wave vector

    A wave vector is a vector representation of a wave. The wave vector has magnitude indicating wavenumber , and the direction of the vector indicates the direction of wave propagation....


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