Two vibrating strings of the same material but lengths L and 2L have radii 2 r and r respectively. They are strectched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency `n_(1)` and the other with frequency `n_(2)`. The ratio `n_(1)//n_(2)` is given by
2
4
8
1

Options

A. 2
B. 4
C. 8
D. 1

Answer

D

Explanation

`n_(1)=(1)/(2l) sqrt([(T)/(4 pi r^(2) rho)])`
and `n_(2) =(1)/(4 l) sqrt([(T)/(pi r^(2) rho)])`
`:. (n_(1))/(n_(2)) = 2xx (1)/(2) =1`.