Question

The ratio of speed of sound in Hydrogen to that in Oxygen at the same temperature is

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

Answer 1

Answer: (B)

$4 : 1$

Answer 2

Speed of sound in a medium is given by
$v = \sqrt{\frac{\gamma P}{\rho}}$
For given temperature, $P_{H_2} = P_{O_2}$
Aslo , $\gamma_{H_2} = \gamma_{O_2}$
$\rho = \frac{m}{V}$
$\therefore \, \, \upsilon \propto \frac{1}{\sqrt{\rho}} \propto \frac{1}{\sqrt{m}}$
or $\frac{ \upsilon_{H_{21}}}{\upsilon_{O_2}} = \sqrt{\frac{m_{O_2}}{m_{H_2}}} = \sqrt{\frac{32}{2}} = \frac{4}{1}$