Question

The constant $\gamma$ for oxygen as well as for hydrogen is 1.40. If the speed of sound in oxygen is 470 m s${}^{-1}$, what will be the speed in hydrogen at the same temperature and pressure?

• A. $1500m{s}^{-1}$
• B. $1880m{s}^{-1}$
• C. $330m{s}^{-1}$
• D. $1000m{s}^{-1}$

Answer 1

The correct option is B

$1880m{s}^{-1}$

The speed of sound in a gas is given by $\sqrt{\frac{\gamma P}{\rho }}$ AT STP, 22.4 litres of oxygen has a mass of 32 g whereas the same volume of hydrogen has a mass of 2 g. Thus, the density of oxygen is 16 times the density of hydrogen at the same temperature and pressure. As γ is same for both the gases,

$\frac{v\left(hydrogen\right)}{v\left(oxygen\right)}=\sqrt{\frac{\rho \left(oxygen\right)}{\rho \left(hydrogen\right)}}$

or, $v\left(hydrogen\right)=4v\left(oxygen\right)$

$=4\times 470m{s}^{-1}=1880m{s}^{-1}$.