A sonometer wire when vibrated in full length has frequency n. Now, it is divided by the help of bridges into a number of segments of lengths `l_(1),l_(2),l_(3)…` when vibrating these segments have frequencies `n_(1), n_(2), n_(3),,,` Then, the correct relation is

Options

A. `n = n_(1) + n_(2) + n_(3) + …..`
B. `n + sqrt(n_(1) xx n_(2) xx n_(3) xx….)`
C. `(1)/(n) = (1)/(n_(1)) + (1)/(n_(2)) + (1)/(n_(3)) + …..`
D. none of the above

Answer

C

Explanation

`n_(1) = (v)/(2l_(1)) , n_(2) = (v)/(2l_(2))`
and `n = (v)/(2l)` (for complete lenglth of wire)
As `l = l_(1) + l_(2) + ….`
`(V)/(2n) = (V)/(2n_(1)) + (V)/(2n_(2)) + ….`
`(1)/(n) = (1)/(n_(1)) + (1)/(n_(2)) + …`