A spring of length l has an elongation `x (lt lt l)`. It carries a transverse wave with speed `v_(1)`. If the spring is cut into two equal halves and any half of the spring is elongated by the distance x, the speed of the transverse wave is `v_(2)`. The value of `v_(1)//v_(2)` is:

Options

A. `1:1`
B. `1:sqrt(2)`
C. `1:2`
D. `2:1`

Answer

B

Explanation

`v_(1)/v_(2) = sqrt(T_(1)/T_(2)) = sqrt((k_(1)x)/(k_(2)x)) = sqrt(k_(1)/k_(2)) = sqrt(k/(2k)) = 1/sqrt(2)`