Question

The density of air at $NTP$ is $1.3\text{g/L}$. Assuming air to be diatomic with $\gamma =1.4$, calculate the velocity of sound in air at ${27}^{\circ }\text{C}$.

• A. $330\text{m/s}$
• B. $300\text{m/s}$
• C. $660\text{m/s}$
• D. $346\text{m/s}$

Answer 1

The correct option is D $346\text{m/s}$

At NTP,
$P=1.013\times {10}^5{\text{N/m}}^2;T=273\text{K}$ and $\rho =1.3\text{g/L}=1.3{\text{kg/m}}^3$
So, velocity of sound in air at NTP is given by
$V=\sqrt{\frac{\gamma P}{\rho }}=\sqrt{\frac{1.4\times 1.013\times {10}^5}{1.3}}=330.29\approx 330\text{m/s}$
Also, we know
$V=\sqrt{\frac{\gamma RT}{M}}$
For same medium
$V\propto \sqrt{T}$
$\Rightarrow \frac{V_1}{V_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}\Rightarrow V_2=\frac{V_1\sqrt{T_2}}{\sqrt{T_1}}=330\frac{\sqrt{273+27}}{\sqrt{273}}$
$\Rightarrow V_2=346\text{m/s}$