# Pipa Organa

## Konsep Dasar

###### Pipa Organa

Pipa organa terbuka

$$f_o = \dfrac {v}{2L}$$

$$f_o : f_1 : f_2 = 1 : 2 : 3$$

Pipa organa tertutup

$$f_o = \dfrac {v}{4L}$$

$$f_o : f_1 : f_2 = 1 : 3 : 5$$

#### Gelombang stationer pada pipa organa terbuka

$$L = \frac 12 \lambda$$

$$\lambda = 2 L$$

$$L = \lambda$$

$$L = \frac 32 \lambda$$

$$\lambda = \frac 23 L$$

Perbandingan panjang gelombang

\begin{equation*} \begin{split} \lambda_o : \lambda_1 : \lambda_2 & = 2L : L : \tfrac 23 L \\\\ \lambda_o : \lambda_1 : \lambda_2 & = 2 : 1 : \tfrac 23 \quad {\color {blue} \times \: 3} \\\\ \lambda_o : \lambda_1 : \lambda_2 & = 6 : 3 : 2 \end{split} \end{equation*}

Perbandingan frekuensi

Frekuensi berbanding terbalik dengan panjang gelombang.

\begin{equation*} \begin{split} f_o : f_1 : f_2 & = \tfrac 16 : \tfrac 13 : \tfrac 12 \quad {\color {blue} \times \: 6} \\\\ f_o : f_1 : f_2 & = 1 : 2 : 3 \end{split} \end{equation*}

#### Gelombang stationer pada pipa organa tertutup

$$L = \frac 14 \lambda$$

$$\lambda = 4 L$$

$$L = \frac 34 \lambda$$

$$\lambda = \frac 43 L$$

$$L = \frac 54 \lambda$$

$$\lambda = \frac 45 L$$

Perbandingan panjang gelombang

\begin{equation*} \begin{split} \lambda_o : \lambda_1 : \lambda_2 & = 4L : \tfrac 43 L : \tfrac 45 L \\\\ \lambda_o : \lambda_1 : \lambda_2 & = 1 : \tfrac 13 : \tfrac 15 \quad {\color {blue} \times \: 15} \\\\ \lambda_o : \lambda_1 : \lambda_2 & = 15 : 5 : 3 \end{split} \end{equation*}

Perbandingan frekuensi

Frekuensi berbanding terbalik dengan panjang gelombang.

\begin{equation*} \begin{split} f_o : f_1 : f_2 & = \tfrac {1}{15} : \tfrac 15 : \tfrac 13 \quad {\color {blue} \times \: 15} \\\\ f_o : f_1 : f_2 & = 1 : 3 : 5 \end{split} \end{equation*}