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 $1.5x$, the speed of sound will be

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

Answer 1

Answer: (A)

$1.22v$

Speed of sound in stretched string
$v=\frac{\overline{T}}{\mu }.....\left(i\right)$
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 Eqs. (i) and (ii)
$v\propto$
$\therefore v^{\prime }=\overline{1.5V}=1.22V$.