Commit 50b091a7 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent c814af0e
Pipeline #15830 canceled with stage
......@@ -1349,11 +1349,11 @@ niveau 2 reprise au 3?
#### Superposition de deux OPPH
* Soient deux OPPH :
* Soient **deux OPPH** :
<br>
$`U_1(\overrightarrow{r},t) = A_1\,cos\big(\omega_1 t + \overrightarrow{k}_1\cdot\overrightarrow{r}+\varphi_1\big)`$
**$`U_1(\overrightarrow{r},t)`$** *$`\;= A_1\,cos\big(\omega_1 t + \overrightarrow{k}_1\cdot\overrightarrow{r}+\varphi_1\big)`$*
<br>
$`U_2(\overrightarrow{r},t) = A_2\,cos\big(\omega_2 t + \overrightarrow{k}_2\cdot\overrightarrow{r}+\varphi_2\big)`$
**$`U_2(\overrightarrow{r},t)`$** *$`\; = A_2\,cos\big(\omega_2 t + \overrightarrow{k}_2\cdot\overrightarrow{r}+\varphi_2\big)`$*
<br>
telles que :
* Les **amplitudes** $`A_1`$ et $`A_2`$ sont *quelconques*.
......@@ -1397,8 +1397,8 @@ $`\quad\;\, = (A_{moy}+ \Delta A_{1-2})\,cos\,\theta_1 + (A_{moy} - \Delta A_{1-
**$`\quad\;\, = A_{moy}\,(cos\,\theta_1 + cos\,\theta_2) + \Delta A_{1-2}\,(cos\theta_1 - cos\theta_2)`$**
* *Travaillons* les **termes de phase** :
* *Travaillons* les **termes de phase** :
<br>
**$`\quad\theta_1(\overrightarrow{r},t)`$**$`\; = \omega_1 t + \overrightarrow{k}_1\cdot\overrightarrow{r}+\varphi_1`$
$`\begin{align}\quad\;\,= \big[ (\omega_{moy}&+ \Delta \omega_{1-2})\, t + \big(\overrightarrow{k}_{moy}+ \Delta \overrightarrow{k}_{1-2}\big)\cdot\overrightarrow{r}\\
......@@ -1409,7 +1409,18 @@ $`\begin{align}
&\quad + \big(\underbrace{\Delta \omega_{1-2} t + \Delta \overrightarrow{k}_{1-2}\cdot\overrightarrow{r}+\Delta\varphi_{1-2}}_{\color{blue}{\theta_{1-2}}}\big)\big]
\end{align}`$
**$`\quad\;\,\theta_{moy}\,+\,\theta_{1-2}`$**
**$`\quad\;\,=\,\theta_{moy}(\overrightarrow{r},t)\,+\,\theta_{1-2}(\overrightarrow{r},t)`$**
<br>
et de la même façon nous obtenons :
<br>
**$`\quad\theta_1(\overrightarrow{r},t)`$**$`\; = \omega_2 t + \overrightarrow{k}_2\cdot\overrightarrow{r}+\varphi_2`$
<br>
$`\quad \cdots`$
<br>
**$`\quad\;\,=\,\theta_{moy}(\overrightarrow{r},t)\,+\,\theta_{1-2}(\overrightarrow{r},t)`$**
......
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