Two vibrating strings of the same material but lengths `L` and `2L` have radii `2r` and `r` respectively. They are stretched under the same tension. Both the string vibrate in their fundamental nodes, the one of length `L` with freuqency `v_(1)` and the other with frequency `v_(2)`. the ratio `v_(1)//v_(2)` is given by

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`.