When a string is divided into three segments of
lengths `l_(1),l_(2) and l_(3)` the fundamental frequencies of
these three segments are `v_(1), v_(2) and v_(3)` respectively.
The original fundamental frequency (v) of the string is

Options

A. `(1)/(sqrt(n)) = (1)/(sqrt(n_(1))) + (1)/(sqrt(n_(2))) + (1)/(sqrt(n_(3)))`
B. `sqrt(n) = sqrt(n_(1)) + sqrt(n_(2)) + sqrt(n_(3))`
C. `n = n_(1) + n_(2) + n_(3)`
D. `(1)/(n) = (1)/(n_(1)) + (1)/(n_(2)) + (1)/(n_(3))`

Answer

D

Explanation

`lambda = lambda_(1) + lambda_(2) + lambda_(3)`
or `l = l_(1) + l_(2) + l_(3)`
Frequency in string `n = (upsilon)/(2l)`
`therefore" "l = (upsilon)/(2n)`
`(upsilon)/(2n) = (upsilon)/(2n_(1)) + (upsilon)/(2n_(2)) + (upsilon)/(2n_(3))`
`(1)/(n) = (1)/(n_(1)) + (1)/(n_(2)) + (1)/(n_(3))`