Question

The velocity of sound through hydrogen is 1400 m s${}^{-1}$ at certain temperature. What will be the velocity of sound through a mixture of 2 parts of volume of hydrogen and 1 part of nitrogen at same temperature?

• A. 150 $\sqrt{3}$ m s${}^{-1}$
• B. 250 $\sqrt{3}$ m s${}^{-1}$
• C. 350 $\sqrt{3}$ m s${}^{-1}$
• D. 450 $\sqrt{3}$ m s${}^{-1}$

Answer 1

The correct option is C 350 $\sqrt{3}$ m s${}^{-1}$

Given

the density of hydrogen $=$ 1
density of nitrogen $=$ 14
Let the volume of the mixture be x
Volume of hydrogen in the mixture
$=\frac{2x}{3}$
Volume of hydrogen in the mixture
$=\frac{2x}{3}\times 1=\frac{2x}{3}$
Mass of oxygen in the mixture $=\frac{x}{3}\times 14$
Total mass of the mixture $=\frac{16x}{3}$
Density of mixture $=\frac{totalmass}{totalvalume}$
$=\frac{16x}{3\left(x\right)}=\frac{16}{3}$
$V\alpha \frac{1}{\sqrt{d}}$
$\therefore \frac{V_1}{V_2}=\sqrt{\frac{d_2}{d_1}}$
$\frac{1400}{V_2}=\sqrt{\frac{16}{3\times 1}}$
$V_2=\frac{1400\sqrt{3}}{4}=350\sqrt{3}m{s}^{-1}$