Question

A closed organ pipe and an open organ pipe are tuned to the same frequency the ratio of their length is

• A. $1:1$
• B. $2:1$
• C. $1:4$
• D. $1:2$

Answer 1

The correct option is D

$1:2$

Step 1: Formula used:

The fundamental tone for an open organ pipe is

${\nu }_o=\frac{v}{2L_o}......\left(1\right)$

Where, $v_o$is the frequency of open organ pipe

$L_o$ is the Length of an open organ pipe

The fundamental tone for a closed organ pipe is

$v_c=\frac{v}{4L_c}......\left(2\right)$

Where, $v_c$is the frequency of open organ pipe

$L_c$ is the Length of a closed organ pipe

Step 2: Find the ratio of length:

As, $\left(1\right)$and $\left(2\right)$ are equal, we get,

$v_o=v_c$

$\Rightarrow \frac{v}{2L_0}=\frac{v}{4L_c}$

$\Rightarrow \frac{L_c}{L_o}=\frac{1}{2}$

The ratio of the length of an open and closed organ pipe is $1:2$

Hence, option D is correct.