Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice of B and the tension in A is half that in B. The ratio of the velocities of waves in A and B is

Options

A. `3 : 2 sqrt 2`
B. `1 : 2sqrt 2`
C. `1 : sqrt 2`
D. `1 : 2`

Answer

B

Explanation

`V= sqrt((T)/(m)) :. (v_(A))/(v_(B)) = sqrt((T_(A))/(T_(B)).(m_(B))/(m_(A)))`
`m_(A) = 4m_(B) (" as " m prop r^(2))`
`:. (v_(A))/(v_(B)) = sqrt((1)/(2).(1)/(4)) = sqrt((1)/(8))`