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 `1.5 x`, 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

Speed of sound in a stretched string
`v=sqrt(T/mu)` ... (i)
where, T is the tension in the string and `mu` is mass per unit
length.
According to Hooke's law `Fprop x `
`therefore T prop x ` ...(ii)
From Eqs. (i) and (ii) `v prop sqrt(x)`
`therefore v' = sqrt(1.5)v = 1.22 v`