A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the…
A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio
$1:2$
$2:3$
$3:4$
$4:5$
Solution
If it is given that First overtone of closed pipe = First overtone of open pipe
$\Rightarrow 3 \left( \frac{\nu}{4 l_{1}} \right) = 2 \left( \frac{\nu}{2 l_{2}} \right)$; where $l_{1}$ and $l_{2}$
are the lengths of closed and open organ pipes hence $\frac{l_{1}}{l_{2}} = \frac{3}{4}$