Fase dan Sudut 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*}
\(\bbox[5px, border: 2px solid red] {\Delta \varphi = \dfrac{\Delta t}{T}}\)
SOAL LATIHAN