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M3P2
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d9e86456
Commit
d9e86456
authored
Mar 26, 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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d9e86456
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@@ -554,7 +554,6 @@ $`\quad\boldsymbol{\mathbf{=\color{brown}{2\,A\cdot cos\Big(\dfrac{\varphi_1-\va
##### 2 - Les ondes sont unidimensionnelles, d'amplitudes différentes, et se propagent dans la même direction
*
Le
*calcul en notation réelle*
est
*très compliqué*
<br>
$
`\Longrightarrow`
$
**notation complexe**
.
*
Une
**onde harmonique réelle $`U_1`$**
s'écrit comme la
*partie réelle de l'onde harmonique complexe $`\underline{U_1}`$*
.
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@@ -563,7 +562,7 @@ $`\quad\boldsymbol{\mathbf{=\color{brown}{2\,A\cdot cos\Big(\dfrac{\varphi_1-\va
&\\
&= \mathscr{Re}\big[A\cdot \big(cos(kx - \omega t + \varphi_1) + i\;sin(kx - \omega t + \varphi_1)\big)\big]\\
&\\
&= \mathscr{Re}\big[A\cdot e^{\,i\;(kx - \omega t + \varphi_1)\big]} \\
&= \mathscr{Re}\big[A\cdot e^{\,i\;(kx - \omega t + \varphi_1)
}
\big]} \\
&\\
&= \mathscr{Re}\big[\underline{U_1}(x,t)\big]
\end{align}`
$
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@@ -575,8 +574,8 @@ $`\quad\boldsymbol{\mathbf{=\color{brown}{2\,A\cdot cos\Big(\dfrac{\varphi_1-\va
<br>
s'écrivent en notation complexe :
<br>
**$`\
underline{U_1}(x,t) = A_1\cdot e^{\,i\;(kx - \omega t + \varphi_1)
}`$**
**$`\
underline{U_2}(x,t) = A_2\cdot e^{\,i\;(kx - \omega t + \varphi_2)
}`$**
**$`\
boldsymbol{\mathbf{\underline{U_1}(x,t) = A_1\cdot e^{\,i\;(kx - \omega t + \varphi_1)}}
}`$**
**$`\
boldsymbol{\mathbf{\underline{U_2}(x,t) = A_2\cdot e^{\,i\;(kx - \omega t + \varphi_2)}}
}`$**
<br>
soit encore :
<br>
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