The extension in a string, obeying Hooke's law, is `x`. The speed of sound in the stretched string is `v`. If the extension in the string is increased to `1.5x`, the speed of sound will be

Options

A. `1.22 v`
B. `0.61 v`
C. `1.50 v`
D. `0.75 v`

Answer

A

Explanation

According to Hooke's law, `F_(g) prop x` [Restoring force `F_(g) = T`, tension of spring]
Velocity of sound by a stretched string
`v = sqrt((T)/(m))`
where `m` is the mass per unit length
`:. (v)/(v') = sqrt((T)/(T')) rArr v'=v sqrt((T')/(T)) = v sqrt((1.5 x)/(x)) = 1.22 v`.