Two wires of the same materila and the same diiamter have their lenghts in the ration `1:3` and are under tension in the ration `1:4` the ratio between the fundametal frequencies is

Options

A. `(5)/(2)`
B. `(3)/(2)`
C. `(2)/(3)`
D. `(2)/(5)`

Answer

B

Explanation

For first wire, `v_(1)=(1)/(2I_(1))sqrt((T_(1))/(m))`
For second wire, `v_(2)=(1)/(v_(2))=(1)/(2I_(2))sqrt((T_(2))/(m))`
`:. (v_(1))/(v_(2))=(I_(2))/(I_(1))sqrt((T_(1))/(T_(2)))=(3)/(1)sqrt((1)/(4))=(3)/(2)`