# Persamaan Gelombang

## Konsep Dasar

#### Persamaan dasar gelombang

$$y = A \sin (\omega t - kx)$$

$$y$$ = simpangan getar

$$x$$ = jarak dari sumber getar

$$A$$ = amplitudo

$$t$$ = waktu getar

$$\omega$$ = kelajuan angular = $$2 \: \pi \: f = \dfrac{2\pi}{T}$$

$$k$$ = bilangan gelombang = $$\dfrac{2\pi}{\lambda}$$

#### Cepat rambat gelombang

$$v = \lambda \:.\: f$$

#### Fase dan sudut fase

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

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

#### 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} \\\\ \Delta \varphi & = \frac{\Delta x}{\lambda} \end{split} \end{equation*}

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} \\\\ \Delta \varphi & = \frac{\Delta t}{T} \end{split} \end{equation*}

#### Cepat getar

$$v_y = \dfrac{dy}{dt} = \omega A \cos (\omega t - kx)$$

$$v_y = \omega \sqrt{A^2 - y^2}$$

#### Percepatan getar

$$a = \dfrac{dv}{dt} = - \omega^2 A \sin (\omega t - kx)$$

$$a = - \omega^2 y$$