Question

At the same temperature, the ratio of the speed of sound in hydrogen to that in oxygen is

• A. $16:1$
• B. $1:4$
• C. $2:3$
• D. $4:1$

Answer 1

The correct option is D

$4:1$

The explanation for the correct option:

D. $4:1$

The expression used for calculating the speed of sound in a medium:

Speed of sound in a medium = $\mathrm{v}=\surd (\mathrm{\gamma P}/\mathrm{\rho })$

For given temp, ${\mathrm{P}}_{{\mathrm{H}}_2}={\mathrm{P}}_{{\mathrm{O}}_2}$

Also,${\mathrm{\gamma }}_{{\mathrm{H}}_2}={\mathrm{\gamma }}_{{\mathrm{O}}_2}$

And, $\mathrm{\rho }=\mathrm{m}/\mathrm{V}$

Therefore,$\mathrm{v}\mathrm{\alpha }1/\surd \mathrm{m}$

$\begin{array}{rcl}{\mathrm{v}}_{{\mathrm{H}}_2}/{\mathrm{v}}_{{\mathrm{O}}_2}& =& \surd (32/2)\\ & =& 4/1\end{array}$

Final Answer: Therefore, option D is the correct option.