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

Answer

D

Explanation

The speed of a wave in a stretched string is
` v = sqrt(T/m) ` ….(1)
As per Hooke's law, extension (x) `propto` tension (T) or `T propto x `
` :. ` from (1), ` v propto sqrtT " and hence " v propto sqrtx`
` :. V_(2)/v_(1) = sqrt((1.5 x)/x) = sqrt(1.5) = 1.22`
` :. v_(2) = (1.22) v_(1) " or " (1.22) ` V