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 is given by `v = (1)/(2l) sqrt((T)/(mu))`
(with both the ends fixed)
`:.` Fundamental frequency `v = prop (1)/(lsqrt(mu))`
[for same tension on both strings]
where `mu` = mass per unit length of wire `= rho.A`
`:. (v_(1))/(v_(2))=((r_(2))/(r_(1)))((l_(2))/(l_(1)))=((r)/(2r))((2L)/(L))=1`.