Question

For a certain organ pipe, three successive resonant frequencies are observed at $425,595$ and $765Hz$. The speed of sound in air is $340m/s$. The pipe is a

• A. closed pipe of length $1m$
• B. closed pipe of length $2m$
• C. open pipe of length $1m$
• D. open pipe of length $2m$

Answer 1

The correct option is A closed pipe of length $1m$

Fundamental frequency, $f=\frac{v}{\lambda }=f_1-f_2$
$\Rightarrow 170=\frac{340}{\lambda }$
$\Rightarrow \lambda =2m$

Ratio of $\frac{n_1}{n_2}=\frac{85}{119}$

$\Rightarrow$ Add frequencies, so organ pipe is closed with length $l=\frac{\lambda }{2}=1m$