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, $v=\sqrt{\frac{\gamma P}{\rho }}$.

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 $\gamma$ is same for both the gases,

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

$\frac{v_{\left(hydrogen\right)}}{v_{\left(oxygen\right)}}=\sqrt{\frac{16}{4}}$

or, $v_{\left(hydrogen\right)}=4v_{\left(oxygen\right)}$

$v_{\left(hydrogen\right)}=4\times 470m{s}^{-1}=1880m{s}^{-1}$.