Tube `A` has both ends open while tube `B` has one closed, otherwise they are identical. The ratio of fundamental frequency of tube `A and B` is

Options

A. `1 : 2`
B. `1 : 4`
C. `2 : 1`
D. `4 : 1`

Answer

C

Explanation

The fundamental frequency for an open pipe is
`f=(v)/(lamda)`
`l=(lamda)/(2),lamda=2l`
`f_("open")=(v)/(2l)`
`l=(lamda)/(4)`
`lamda=4l,f_("closed")=(v)/(lamda)=(v)/(4l)`
`(f_("open"))/(f_("closed"))=(f_(A))/(f_(B))=(v)/(2l)xx(4l)/(v)=2:1`