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

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

Tardigrade Admin · Accepted Answer

If it is given that First overtone of closed pipe = First overtone of open pipe

\Rightarrow 3 (\frac{ν}{4 l _{1}}) = 2 (\frac{ν}{2 l _{2}}); w h ere l_{1} an d l_{2}

are the lengths of closed and open organ pipes hence

\frac{l _{1}}{l _{2}} = \frac{3}{4}

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