Question

The extension in a string obeying Hooke's law $v$ 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

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

Answer 1

The Correct Option is A

Speed of sound $V =\sqrt{\frac{ T }{\mu}}$
Also $V \propto \sqrt{ T }$
So $T \propto x$
$\frac{ V _{2}}{ V _{1}}=\sqrt{\frac{1.5 x }{ x }}$
$V _{2}=\sqrt{1.5} \,V =1.22\, V$