`n_(1)` is the frequency of the pipe closed at one and `n_(2)` is the frequency of the pipe open at both ends. If both are joined end to end, find the fundamental frequency of closed pipe so formed

Options

A. `(n_(1) n_(2))/(n_(2) + 2n_(1))`
B. `(n_(1) n_(2))/(2n_(2) + n_(1))`
C. `(n_(1) + 2n_(2))/(n_(2) n_(1))`
D. `(2n_(1) + n_(2))/(n_(2)n_(1))`

Answer

A

Explanation

Frequency of closed pipe , `n _(1) = (v)/(4l_(1)) implies l _(1) = (v)/(4n_(1))`
Frequency of one pipe , `n_(2) = (v)/(2l_(1)) implies l_(2) = (v)/(2n_(2))`
when both pipe are joined them length of closed pipe
l `= l_(1) + l_(2)`
`(v)/(4n) = (v)/(4n_(1)) + (v)/(2n_(2))`
or `(1)/(2n) = (1)/(2n_(1)) + (1)/(n_(2))`
or `(1)/(2n) - (n_(2) + 2n_(1))/(2n_(1) n_(2)) `
or `n = (n_(1) n_(2))/(n_(2) + 2n_(1))`