Q. 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
A) $1.22\ v$
B) $0.61\ v$
C) $1.50\ v$
D) $0.75\ v$
Explanation
(a) Speed of sound in a stretched string $v = \sqrt{\frac{T}{\mu}}$ …(i)
Where $T$ is the tension in the string and $\mu$ is mass per unit length
According to Hooke’s law, $F \propto x\therefore T \propto x$ …(ii)
From (i) and (ii), $v \propto \sqrt{x}$
$\therefore v^{'} = \sqrt{1.5}\ v = 1.22\ v$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.