Question

Find the speed of sound in $H_2$ gas if the speed of sound in $O_2$ gas is $450\text{m/s}$ at the same temperature.

• A. $1800\text{m/s}$
• B. $1200\text{m/s}$
• C. $1500\text{m/s}$
• D. $1600\text{m/s}$

Answer 1

The correct option is A $1800\text{m/s}$

We know that the velocity of sound in any medium is given by,
$v=\sqrt{\frac{\gamma RT}{M}}$
Since temperature is same for both the gases and both the gases are diatomic,
So, $\frac{v_{H_2}}{v_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{H_2}}}$
$\Rightarrow \frac{v_{H_2}}{v_{O_2}}=\sqrt{\frac{32}{2}}=4$
$\Rightarrow v_{H_2}=4\times v_{O_2}=4\times 450=1800\text{m/s}$