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. 8
B. 4
C. 2
D. 1

Answer

D

Explanation

`v_(1)/v_(2) = (4L)/(2L) sqrt(T/m_(1) xx m_(2)/T)`
` = 2 sqrt(m_(2)/m_(1) ) " but " m_(2)/m_(1) = (pir_(2)^(2)rho )/(pi r _(1)^(2) rho) = 1/4 `
` :. v_(1)/v_(2) = 2 xx sqrt(1/4) = 1 " " :. v_(1) = v_(2) `