Question

The velocity of sound in a gas is $30m{s}^{-1}$ at $27K$. What is the velocity of the sound in the same gas at $127K$?

• A. $20m{s}^{-1}$
• B. $30m{s}^{-1}$
• C. $20\sqrt{3}m{s}^{-1}$
• D. $65m{s}^{-1}$

Answer 1

Answer: (D)

$65m{s}^{-1}$

Velocity of sound in gaseous medium $v\propto \sqrt{T}$
Thus we get $\frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}$
Given : $v_1=30m/s$ $T_2=127K$ and $T_1=27K$
$\therefore$ $\frac{v_2}{30}=\sqrt{\frac{127}{27}}$
$⟹v_2\approx 65m/s$
Thus option D is correct.