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. `N/4`
B. `sqrt2n`
C. n
D. `n/sqrt2`

Answer

C

Explanation

`n=1/"2l"sqrt(T/(pir^2rho))`
`rho_1=rho/2, T^1=2T`and `D^1=2D` `r_1=2r`
`n^1=1/"2l"sqrt((2T)/(pi(2r)^2rho/2))=1/"2l"sqrt((1)/(pir^2rho))=n`
`rArr` No change