Question

A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio

• A. 1:2
• B. 2:3
• C. 3:4
• D. 4:5

Answer 1

The correct option is C 3:4

An overtone is any frequency higher than the fundamental frequency of a sound.
First overtone for open pipe:
${\nu }_{o1}=\frac{2v}{2l_o}$

First overtone for closed pipe:
${\nu }_{c1}=\frac{3v}{4l_c}$

${\nu }_{o1}={\nu }_{c1}\Rightarrow \frac{l_c}{l_o}=\frac{3}{4}$