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

Fundamental frequency `n=(1)/(2l)sqrt((T)/(pir^2rho))`
where `m=` mass per unit length of wire
`impliesnprop=(1)/(lr)implies(n_1)/(n_2)=(r_2)/(r_1)xx(l_2)/(l_1)=(r)/(2r)xx(2L)/(L)=(1)/(1)`