Question

The speed of sound in hydrogen at $NTP$ is $1270{ms}^{-1}$. Then the speed in a mixture of hydrogen and oxygen in the ratio $4:1$ by volume will be

• A. $317{ms}^{-1}$
• B. $635{ms}^{-1}$
• C. $830{ms}^{-1}$
• D. $950{ms}^{-1}$

Answer 1

Answer: (B)

$635{ms}^{-1}$

In Hydrogen, $v_H=\sqrt{\frac{\gamma P}{{\rho }_H}}$

In mixture, $v_M=\sqrt{\frac{\gamma P}{{\rho }_M}}$

Now density of mixture, ${\rho }_m=\frac{Massofmixture}{Volumeofmixture}=\frac{{\rho }_O{V}_O+{\rho }_H{V}_H}{V_O+V_H}=\frac{{\rho }_H[V_O\frac{{\rho }_O}{{\rho }_H}+4V_O]}{V_O+4V_O}$ as $(V_O:V_H=1:4)$

or $\frac{{\rho }_M}{{\rho }_H}=4$

Thus, $\frac{v_M}{v_H}=\sqrt{\frac{{\rho }_H}{{\rho }_M}}=\frac{1}{2}$

or $v_M=\frac{1}{2}\times 1270=635m/s$