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

Answer 1

Answer: (A)

Speed of sound in a stretched string
$v=\sqrt{\frac{T}{\mu }} \, \ldots \left(i\right)$
Where T is the tension and $\mu $ is mass per unit length.
According to Hooke's law, $F \propto x$
$T \propto x \, \ldots \left(i i\right)$
From Eqs. (i) and (ii)
$v \propto \sqrt{x}$
$v^{′}=\sqrt{1.5}v=1.22 \, v$