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M3P2
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100289c5
Commit
100289c5
authored
May 01, 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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100289c5
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@@ -1669,16 +1669,18 @@ $`= 2\,A\,\,cos\big(\Delta \omega_{1-2} t + \varphi_B) \times cos\,(\omega_{moy}
J'admet ici que cette intensité est proportionnelle au carré de l'onde acoustique
_(voir le point culturel sur l'acoustique dans la partie "au-delà")._.
Mon ouïe n'étant sensible
qu'au terme de battement, l'intervalle temporel
**$`
T
`$**
qui
**sépare deux minima consécutifs**
d'intensité correspond à un
qu'au terme de battement, l'intervalle temporel
**$`
\mathbf{T}
`$**
qui
**sépare deux minima consécutifs**
d'intensité correspond à un
*écart de $`\pi`$ entre leurs phases*
:
<br>
$
`U(t)=U(t+T)\Longleftrightarrow cos^2\left(2\pi\dfrac{\nu_1 - \nu_2}{2} t + \varphi_B\right)=cos^2\left(2\pi\dfrac{\nu_1 - \nu_2}{2} t + \varphi_B + \pi\right)`
$
$
`cos\left(2\pi\dfrac{\nu_1 - \nu_2}{2} t + \varphi_B\right)
**$`\mathbf{U(t)=U(t+T)}`$**
<br>
$
`\quad\Longleftrightarrow cos^2\left(2\pi\dfrac{\nu_1 - \nu_2}{2} t + \varphi_B\right)=cos^2\left(2\pi\dfrac{\nu_1 - \nu_2}{2} (t\mathbf{\color{blue}{+T}}) + \varphi_B + \pi\right)`
$
<br>
$
`\quad\Longleftrightarrow cos^2\left(\pi (\nu_1 - \nu_2) t + \varphi_B\right)=cos^2\left(\pi (\nu_1 - \nu_2) t + \varphi_B + \pi\right) \mathbf{\color{blue}{+ \pi}}`
$
<br>
$
`\quad\Longleftrightarrow 2\pi\dfrac{\nu_1 - \nu_2}{2} T = \pi`
$
<br>
**$`\quad\Longleftrightarrow \mathbf{T = |\nu_1 - \nu_2|}`$**
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