# Fase dan Sudut Fase

## Konsep Dasar

###### Fase, Sudut Fase dan Beda Fase

Fase

$$\varphi = \dfrac tT - \dfrac {x}{\lambda}$$

Sudut Fase

$$\theta = \omega t - kx$$

Beda Fase Dua Titik Berbeda Pada Waktu Yang sama

$$\Delta \varphi = \dfrac{\Delta x}{\lambda}$$

Beda Fase Suatu Titik Pada Waktu Yang Berbeda

$$\Delta \varphi = \dfrac{\Delta t}{T}$$

#### Fase dan Sudut Fase

Pada suatu persamaan gelombang, $$y = A \sin (\omega t - kx)$$

$$\omega t - kx$$ disebut sudut fase $$(\theta)$$.

$$\bbox[5px, border: 2px solid red] {\theta = \omega t - kx}$$

\begin{equation*}
\begin{split}
y & = A \sin (\omega t - kx) \\\\
y & = A \sin (2 \pi \:.\: f \:.\: t - \frac {2\pi}{\lambda} \:.\: x) \\\\
y & = A \sin 2 \pi (f \:.\: t - \frac {1}{\lambda} \:.\: x) \\\\
y & = A \sin 2 \pi \left(\frac tT - \frac {x}{\lambda} \right)
\end{split}
\end{equation*}

$$\dfrac tT - \dfrac {x}{\lambda}$$ disebut fase gelombang.

$$\bbox[5px, border: 2px solid red] {\varphi = \dfrac tT - \dfrac {x}{\lambda}}$$

#### Beda Fase

Beda fase 2 titik berbeda pada waktu yang sama

\begin{equation*} \begin{split} \Delta \varphi & = \varphi_2 - \varphi_1 \\\\ \Delta \varphi & = \left(\frac{t}{T} - \frac{x_2}{\lambda}\right) - \left(\frac{t}{T} - \frac{x_1}{\lambda}\right) \\\\ \Delta \varphi & = \cancel {\frac{t}{T}} - \frac{x_2}{\lambda} - \cancel {\frac{t}{T}} + \frac{x_1}{\lambda} \\\\ \Delta \varphi & = \frac{x_1 - x_2}{\lambda} \end{split} \end{equation*}

$$\bbox[5px, border: 2px solid red] {\Delta \varphi = \dfrac{\Delta x}{\lambda}}$$

Beda fase suatu titik pada waktu yang berbeda

\begin{equation*} \begin{split} \Delta \varphi & = \varphi_2 - \varphi_1 \\\\ \Delta \varphi & = \left(\frac{t_2}{T} - \frac{x}{\lambda}\right) - \left(\frac{t_1}{T} - \frac{x}{\lambda}\right) \\\\ \Delta \varphi & = \frac{t_2}{T} - \cancel {\frac{x}{\lambda}} - \frac{t_1}{T} + \cancel {\frac{x}{\lambda}} \\\\ \Delta \varphi & = \frac{t_2 - t_1}{T} \end{split} \end{equation*}

$$\bbox[5px, border: 2px solid red] {\Delta \varphi = \dfrac{\Delta t}{T}}$$