Question

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is
A. `1:2`
B. `2:1`
C. `2:3`
D. `4:3`

Answer 1

Correct Answer - A
Let `l_1` and `l_2` be the lengths of closed and open pipes respectively. (neglecting end correction)
`l_1=(lamda_1)/(4)implieslamda_1=4l_1` and `l_2=(lamda_2)/(2)implieslamda_2=2l_2`
Given `n_1=n_2` so `(v)/(lamda_1)=(v)/(lamda_2)implies(v)/(4l_1)=(v)/(2l_2)=(l_1)/(l_2)=(1)/(2)`