The stirng stretched by tension T and length L vibrates in resonance with a tuning fork of frequency n. the tension in the stretched string is increased by 69% and length of string reduced by 35%. Then, the frequency of vibrating string is

Options

A. n
B. `1.5`n
C. 2n
D. `n//2`

Answer

C

Explanation

`n_(1) = 1/(2l_(1)) sqrt(T_(1)/m) ` ( In the first case) …(1)
In the second case , T is increased by `69%`
i.e. `T_(2) = 169/100 T_(1) `
and the lenth is decreased by 35 %
or `l_(2)/l_(1) = 65/100 = 13/20 :. l_(1)/l_(2) = 20/13 `
` :. n_(2) = 1/(2l_(2)) sqrt(T_(2)/m) ` ....(2)
`:. n_(2)/n_(1) = (2l_(1))/(2l_(2)) sqrt((169T_(1))/(100 m)xx m/T_(1)) `
` = 20/1 sqrt(169/100) = 20/13 xx 13/10 = 2 `
` :. n_(2) = 2n_(1) " or " n_(2) =2 n `