Question

The extension in a string, obeying Hook'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 :

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

Answer 1

The correct option is A

1.22 v

From Hooke's law

Tension in a string ($T$) $\propto$ extension ($x$)

and speed of sound in string $v$ $\propto$ $\sqrt{T}$

Therefore, $v\propto \sqrt{x}$

$X$ is increased to 1.5 times i.e., speed will increase by $\sqrt{1.5}$ times or 1.22 times. Therefore, speed of Sound in new position will be 1.22 v.