Question

The velocity of sound in a gas at a temperature ${27}^{\circ }\text{C}$ is $v$. In the same gas, its velocity will be $2v$ at temperature

• A. ${727}^{\circ }\text{C}$
• B. ${827}^{\circ }\text{C}$
• C. ${927}^{\circ }\text{C}$
• D. ${627}^{\circ }\text{C}$

Answer 1

The correct option is C ${927}^{\circ }\text{C}$

We know that, velocity of sound in gas,
$v=\sqrt{\frac{\gamma RT}{M}}$
For the same gas in the same medium,
$v\propto \sqrt{T}$
So, $\frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$
$\Rightarrow \frac{v}{2v}=\sqrt{\frac{(27+273)}{T_2}}$
$\Rightarrow T_2=1200\text{K}={927}^{\circ }\text{C}$

$\begin{array}{c}\text{Why this question?}\\ \text{Tips: For the same gas, molecular weight (M) and}\gamma \\ \text{is fixed.}\end{array}$