Wavelength - SpeedyLook encyclopedia

Definition

A wave is a physical phenomenon being propagated and which reproduces identical to itself a little later in time and a little further in space. One can then define the wavelength as being the short distance separating two points of the wave strictly identical to a given moment.

One commonly indicates it by the Greek letter λ (Lambda).

The wavelength is the space equivalent of the temporal Period. Indeed, the wavelength is the distance covered by the wave during one period. If one calls C the Célérité of the wave and T his period temporal, one a:

\ lambda = C T = \ frac {C} {\ naked}

Approaches mathematical

Mathematically, one can define it as follows: if the wave can be represented by a periodic function F which takes as argument distance X, then the wavelength is smallest λ > 0 such as for any X, one has:

\ displaystyle {F (x+ \ lambda) = F (X)}

By analogy with the homonymous mathematical concept, one names it also sometimes improperly period. In Physical, the period is the temporal equivalent wavelength: the period is the minimal time which passes between two identical repetitions of the wave in the same point. For a sinusoidal wave, the wavelength is the distance between two successive peaks of the same sign :

The axis X represents the distances covered, and is there the value at a given moment of a quantity which varies (for example pressure of the air for a sound wave or intensity of the electric field or magnetic of a light wave).

The wavelength is proportional to the period, and thus inversely proportional to the Fréquence, the number of tops of the same sign which cross a point in one one second duration. The wavelength is equal at the speed of the wave divided by the frequency of passage.

Vector of wave and number of wave

With each wavelength is associated a number of wave and a vector with wave.

the Nombre of wave is a size proportional to the number of oscillations which a Onde by a unit of length carries out: it is the number wavelengths present on a distance from $2 \ pi$ units of length. This Nombre of wave is thus a size inversely proportional to the wavelength. Its unit is the Radian by Mètre.

the Vecteur of wave (or “vector of phase”, in electronics in particular) is a Vecteur representing a Onde. The standard of the vector corresponds to the Nombre of wave (dependant contrary the wavelength), and its direction indicates the direction of propagation of the Onde.

The vector of wave is very useful to generalize the equation of a Onde with the description of a family of waves. If all the waves of a family are propagated in the same direction and have the same wavelength, they all can be described by the same vector of wave. The case more the current of a family of wave observing these conditions is that of a plane Onde, for which the family of waves is also coherent (all the waves have same the phase).

Electromagnetic wave

Example wavelength

Wavelength of Broglie

Louis de Broglie discovered that all the physical particles equipped with a Quantité of movement have a wavelength, named wavelength of Broglie (see the article Wave mechanics). For a relativistic particle , the wavelength of Broglie is given by

\ lambda = \ frac {H} {p} = \ frac {H} {\ gamma mv} = \ frac {H} {m_0v} \ sqrt {1 - \ frac {v^2} {c^2}}

where $~h~$ is the Constante of Planck, $~ \ gamma~$ the factor of Lorentz, $~m_0~$ the mass of the particle at rest, $~v~$ speed, and $~c~$ speed of light in the vacuum.

Thermal wavelength of Broglie

Internal bonds

Simple: Wavelength

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