If the tension and diameter of a sonometer wire of fundamental frequency `n` are doubled and density is halved then its fundamental frequency will become

Options

A. 2n
B. n
C. `n/sqrt2`
D. `3n `

Answer

B

Explanation

`n = 1/(2L) sqrt(T/(pi r^(2) rho)) :. n_(2)/n_(1) = sqrt(T_(2)/T_(1) xx (r_(1)/r_(2))^(2) xx rho_(1)/rho_(2))`
` = sqrt( 2 xx 1/4 xx 2/1 ) = 1 :. n_(2) = n_(1) `