A stretched wire of stone length under a tension is vibrating with its fundamental frequency . Its length is decreased by `45 %` and tension is increased by `21 %` . Now fundamental frequency

Options

A. increases by `50 %`
B. increases by `100 %`
C. decreases by `50 %`
D. decreases by `25 %`

Answer

B

Explanation

`n_(1) = (1)/( 2l_(1)) sqrt((T_(1))/(m)) , n_(2) = (1)/( 2l_(2)) sqrt((T_(2))/(m))`
`:. (n_(2))/(n_(1)) = (l_(1))/(l_(2)) sqrt ((T_(2))/(T_(1)))`
Let
`l_(1) = 100 l , l_(2) = 55 l`
`T_(1) = 100 T , T_(2) = 121 T`
`:. (n_(2))/(n_(1)) = (100 l)/(55 l) sqrt((121 T)/( 100 T))`
` = (100)/(55) xx (11)/(10) = 2`
`:. n_(2) =2 n_(1)`