Two vibrating string of the same material but length L and 2L have radii 2r and r respectively. Then are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency` 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`.