Commit 6afdc537 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 0e4b4338
Pipeline #18810 canceled with stage
......@@ -483,36 +483,36 @@ matériel à la vitesse $`\mathscr{v}_{prop}`$, tu as une deuxième relation :
* Tu obtiens ainsi :
<br>
**$`\mathbf{d_{impuls.2} = d_{impuls.1}}`$** *$`\mathbf{\, + d_{source} + d_{capteur}}`$*
<br>
<br><br>
$`\begin{align}
\underbrace{\mathscr{v}_{propag.}\cdot (t_2' - t_2)}_{\color{blue}{d_{impuls.2}}}&=
\underbrace{\mathscr{v}_{propag.}\cdot (t_1' - t_1)}_{\color{blue}{d_{impuls.1}}}\\
& \hspace{1cm} + \underbrace{\mathscr{v}_{source}\cdot (t_2 - t_1)}_{\color{blue}{d_{source}}}\\
& \hspace{2cm} +\underbrace{\mathscr{v}_{capteur}\cdot (t_2' - t_1')}_{\color{blue}{d_{capteur}}}
\end{align}`$
<br>
<br><br>
$`\begin{align}
\mathscr{v}_{propag.}\,t_2' - \mathscr{v}_{propag.}\,t_2 &= \mathscr{v}_{propag.}\,t_1' - \mathscr{v}_{propag.}\,t_1\\
& \hspace{0.6cm} + \mathscr{v}_{source}\,t_2 - \mathscr{v}_{source}\,t_1\\
& \hspace{1.2cm} +\mathscr{v}_{capteur}\,t_2' - \mathscr{v}_{capteur}\,t_1'
\end{align}`$
<br>
<br><br>
$`\begin{align}
&\mathscr{v}_{propag.}\,t_2' - \mathscr{v}_{propag.}\,t_1' - \mathscr{v}_{capteur}\,t_2'+ \mathscr{v}_{capteur}\,t_1'\\
& \hspace{1cm} = \mathscr{v}_{propag.}\,t_2 - \mathscr{v}_{propag.}\,t_1 + \mathscr{v}_{source}\,t_2 - \mathscr{v}_{source}\,t_1
\end{align}`$
<br>
<br><br>
$`\begin{align}
&\mathscr{v}_{propag.}\,(t_2' - t_1') - \mathscr{v}_{capteur}\,(t_2' - t_1') \\
&\hspace{1cm} = \mathscr{v}_{propag.}\,(t_2 - t_1) - \mathscr{v}_{source}\,(t_2 - t_1)
&\hspace{1cm} = \mathscr{v}_{propag.}\,(t_2 - t_1) + \mathscr{v}_{source}\,(t_2 - t_1)
\end{align}`$
<br>
<br><br>
$`\begin{align}
& (t_2' - t_1')\; (\mathscr{v}_{propag.} - \mathscr{v}_{capteur})\\
&\hspace{1cm} = (t_2 - t_1)\;(\mathscr{v}_{propag.}- \mathscr{v}_{source})
&\hspace{1cm} = (t_2 - t_1)\;(\mathscr{v}_{propag.}+ \mathscr{v}_{source})
\end{align}`$
<br>
$`\boldsymbol{\mathbf{(t_2' - t_1')= (t_2 - t_1)\cdot \dfrac{\mathscr{v}_{propag.}- \mathscr{v}_{source}}
<br><br>
$`\boldsymbol{\mathbf{(t_2' - t_1')= (t_2 - t_1)\cdot \dfrac{\mathscr{v}_{propag.}+ \mathscr{v}_{source}}
{\mathscr{v}_{propag.} - \mathscr{v}_{capteur}}}}`$
......
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