Update cheatsheet.fr.md

12.temporary_ins/69.waves/30.n3/20.overview/cheatsheet.fr.md

@@ -1446,18 +1446,20 @@ $`\quad\quad \;\; = \cdots`$
 
 * Nous obtenons l'**expression finale** de l'onde résultante de la *superposition de deux OPPH* quelconques :   
   <br>
-  $`\begin{array}\quad = &A_1\,cos\big(\underbrace{\omega_1 t + \overrightarrow{k}_1\cdot\overrightarrow{r}+\varphi_1}_{\color{blue}{\theta_1(\vec{r},t)}}\big)\\
-  &+ A_2\,cos\big(\underbrace{\omega_2 t + \overrightarrow{k}_2\cdot\overrightarrow{r}+\varphi_2}_{\color{blue}{\theta_2(\vec{r},t)}}\big)\end{array}`$   
+  **$`U(\overrightarrow{r},t)`$**  
+  <br>
+  *$`\begin{array}\quad = &A_1\,cos\big(\underbrace{\omega_1 t + \overrightarrow{k}_1\cdot\overrightarrow{r}+\varphi_1}_{\color{blue}{\theta_1(\vec{r},t)}}\big)\\
+  &+ \;A_2\,cos\big(\underbrace{\omega_2 t + \overrightarrow{k}_2\cdot\overrightarrow{r}+\varphi_2}_{\color{blue}{\theta_2(\vec{r},t)}}\big)
+  \end{array}`$*   
   <br>
   $`\begin{array}\quad = &+\,2\,A_{moy}\,cos\,\theta_{moy}\;cos\,\Delta\theta_{1-2}\\
    &-\,2\,\Delta A_{1-2}\,\,sin\,\theta_{moy}\;sin\,\Delta\theta_{1-2}\end{array}`$   
   <br>
-  $`\begin{array}\quad = &+\,2\,A_{moy}\,cos\big(\omega_{moy} t + \overrightarrow{k}_{moy}\cdot\overrightarrow{r}+ \varphi_{moy}\big)\\
-    &\quad\times\,cos\(\Delta \omega_{1-2} t + \Delta \overrightarrow{k}_{1-2}\cdot\overrightarrow{r}+\Delta\varphi_{1-2}\big)\\
-    \\
-   &\quad = -\,2\,sin\big(\omega_{moy} t + \overrightarrow{k}_{moy}\cdot\overrightarrow{r}+ \varphi_{moy}\big)\\
-    &\quad\times\,sin\(\Delta \omega_{1-2} t + \Delta \overrightarrow{k}_{1-2}\cdot\overrightarrow{r}+\Delta\varphi_{1-2}\big)
-    \end{array}`$
+  **$`\begin{array}\quad = &+\,2\,A_{moy}\,cos\big(\omega_{moy} t + \overrightarrow{k}_{moy}\cdot\overrightarrow{r}+ \varphi_{moy}\big)\\
+    &\quad\times\,cos\big(\Delta \omega_{1-2} t + \Delta \overrightarrow{k}_{1-2}\cdot\overrightarrow{r}+\Delta\varphi_{1-2}\big)\\
+   &-\,2\,sin\big(\omega_{moy} t + \overrightarrow{k}_{moy}\cdot\overrightarrow{r}+ \varphi_{moy}\big)\\
+    &\quad\times\,sin\big(\Delta \omega_{1-2} t + \Delta \overrightarrow{k}_{1-2}\cdot\overrightarrow{r}+\Delta\varphi_{1-2}\big)
+    \end{array}`$**