Two pipes have equal length of 2m, one is closed at one end and the other is open at both ends. The speed of sound in air is `340m//s`. At what frequency will both the pipes resonate ?

Explanation

Here, `l=2m, upsilon=340m//s.`
Resonant frequencies for closed organ pipe are
`f_(1)=((2n_(1)-1)upsilon)/(4l), ` where `n_(1)=1,2,3…`
`f_(1)=(upsilon)/(4l), (3upsilon)/(4l),(5upsilon)/(4l)` …etc.
Resonant frequencies for open organ pipe are
`f_(2)=(n_(2)upsilon)/(2l),` where `n_(2)=1,2,3.....`
`:. f_(2)=(upsilon)/(2l),(2upsilon)/(2l), (3upsilon)/(2l), (4upsilon)/(2l)` ...etc.
Comparing values of `f_(1)` and `f_(2)`, we find that there is no common frequency at which the two pipes can resonate.