A string is cut into three parts, having fundamental frequencies `n_(1),n_(2)` and `n_(3)` respectively. Then original fundamental frequency 'n' related by the expression as (other quantities are identical) :-

Options

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

Answer

A

Explanation

`n_(1)l_(1)=n_(2)l_(2)=n_(3)l_(3)=nl`
`rArr l_(1)+l_(2)=l_(3)=lrArr (nl)/(n_(1))+(nl)/(n_(2))+(nl)/(n_(3))=l`
`rArr (1)/(n)=(1)/(n_(1))+(1)/(n_(2))+(1)/(n_(3))=l`
`rArr (1)/(n)=(1)/(n_(1))+(1)/(n_(2))+(1)/(n_(3))`