In a pipe opened at both ends `n_(1)` and `n_(2)` be the frequencies corresponding to vibrating lengths `L_(1)` and `L_(2)` respectively .The end correction is

Options

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

Answer

C

Explanation

If e the end correction for the pipe closed at one end, then for the open pipe, end correction is 2e.
` :. L_(1) " and L_(2)` are the corrected lengths
where `L_(1) = l_(1) + 2e " and " L_(2) = l_(2) + 2e`
and ` v = 2n_(1) L_(1) = 2n_(2) L_(2)`
` :. n_(1)(l_(1) + 2e) = n_(2) (l_(2) + 2e)`
` :. n_(1)l_(1) + 2 en _(1) = n_(2) l_(2) + 2en_(2)`
`:. n_(2)l_(2) - n_(1)l_(1) = 2e (n_(1) - n_(2)) " if " n_(1) gt n_(2) `
` :. e = (n_(2) l_(2) - n_(1) l_(1))/(2(n_(1) - n_(2)))`