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