In Physical, the number of wave is a size proportional to the number of oscillations which a wave by a unit of length carries out: it is the number of wavelengths present on a distance from $2\; \backslash \; pi$ units of length. This number of wave is thus a size inversely proportional to the wavelength. Its unit is the Radian by Mètre. It is the space equivalent of the concept of Pulsation used for a size oscillating temporally. The application of a transformation of Fourier on data functions of time produces a spectrum according to the Fréquence; its application on the data functions of space coordinates (of the position) produced a spectrum according to the number of wave.

The exact definition of the number of wave depends on the scientific discipline in which it is used.

In physics

In general, the number of wave K is most frequently defined by:

$k\; \backslash \; equiv\; \backslash \; frac\; \{2\; \backslash \; pi\}\; \{\backslash \; lambda\}\; =\; \backslash \; frac\; \{2\; \backslash \; pi\; \backslash \; naked\}\; \{v\_p\}\; =\; \backslash \; frac\; \{\backslash \; Omega\}\; \{v\_p\}\; \backslash ,$

• λ is the Wavelength.
• ν is the Fréquence.
• v_p is the Speed of phase of the wave (also called Célérité).
• ω is the angular Fréquence or pulsation.

The concept of number of wave is closely related to that of Vecteur of wave.

One can also allot a number of wave to a material particle of average impulse p, by using the relation of of Broglie:

$k\; \backslash \; equiv\; \backslash \; frac\; \{p\}\; \{\backslash \; hbar\}$

In spectroscopy

In Spectroscopy, the number of wave $\backslash \; naked\; tilde\; \{\backslash \}$ (also noted $\backslash \; sigma$) is the number of oscillations of the wave per unit of length, it is thus defined as:

$\backslash \; naked\; tilde\; \{\backslash \}\; =\; 1\; \backslash \; lambda\; \backslash ,$

where λ is the wavelength in the Vide measured in cm. The unit of the number of wave is thus the cm^-1 .

For example, the numbers of wave of the emission lines of the Atome of Hydrogène are given by:

$$

\ naked tilde {\} = R \ left ({1 \ over} - {1 \ over} \ right) \,

• R is the Constante of Rydberg
• n₁ and n₂ is the numbers of the orbital with n₂ > n₁.

Atmospheric sciences

Into sciences of the atmosphere, the number of wave definite like the length of the space field is divided by the Wavelength, which is equivalent to the number of times where a wave with very the phase on the whole of the space field. The space field can be 2π in a zero-dimensional case, or

$2\; \backslash \; pi\; R\; \backslash \; cos\; \backslash \; left\; (\backslash \; phi\; \backslash \; right)\; \backslash ,$

for a wave in the atmosphere, with R the ray of the Ground and φ the Latitude. The diagrams number of wave-frequency are an average current to represent the waves in the atmosphere.

See too

• Wave

• Vector of wave
• Directivity

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