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M3P2
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7f15d000
Commit
7f15d000
authored
Apr 12, 2023
by
Claude Meny
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Update cheatsheet.fr.md
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12.temporary_ins/69.waves/30.n3/20.overview/cheatsheet.fr.md
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7f15d000
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@@ -429,16 +429,21 @@ RÉSUMÉ
*
*Relations entre les propriétés*
temporelles, spatiales et du milieu :
<br>
**$`\large{\boldsymbol{\mathbf{k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{\mathscr{v} T} = \dfrac{2\pi\,\nu}{T} = \dfrac{\omega}{\mathscr{v}}}}}`$**
<br><br>
!!!!
*Attention*
!!!!
!!!! Parfois dans la littérature, le terme
*nombre d'onde*
est défini par $
`k = 1\,/\,\lambda`
$.
!!!! Il diffère d'un facteur $
`2\pi`
$ de la définition ici donnée.
<br><br>
*
Cas d'une
*onde unidimensionnelle*
:
<br>
**$`U(\vec{r}, t) = A \cdot cos(\omega t - kx + \varphi)`$**
*
Une OPPH peut aussi s'écrire en utilisant la fonction sinus. Nous avons alors, pour une :
OPPH 1D :
$
`
U(\vec{r}, t) = A\cdot \sin(\omega t - kx + \varphi)
`
$
$
`
\boldsymbol{\mathbf{U(\vec{r}, t) = A\cdot \sin(\omega t - kx + \varphi)}}
`
$
OPPH 2D ou 3D :
$
`
U(\vec{r}, t) = A \cdot \sin(\omega t - \vec{k}\cdot\vec{r} + \varphi)
`
$
$
`
\boldsymbol{\mathbf{U(\vec{r}, t) = A \cdot \sin(\omega t - \vec{k}\cdot\vec{r} + \varphi)}}
`
$
...
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