Question

Speed of sound in air is $332\text{m/s}$ at NTP. What will be the speed of sound in hydrogen at NTP if the density of hydrogen at NTP is $\left(1/16\right)$ that of air?

• A. $664\text{m/s}$
• B. $1328\text{m/s}$
• C. $1155\text{m/s}$
• D. $166\text{m/s}$

Answer 1

The correct option is B $1328\text{m/s}$

The velocity of sound in a medium is given by
$v=\sqrt{\frac{\gamma P}{\rho }}$
Velocity of sound in air is
$v_{air}=\sqrt{\frac{{\gamma }_{air}{P}_{air}}{{\rho }_{air}}}$ ...(i)
Velocity of sound in hydrogen is
$v_H=\sqrt{\frac{{\gamma }_H{P}_H}{{\rho }_H}}$ ...(ii)

From equation (i) and (ii)
$\frac{v_H}{v_{\text{air}}}=\sqrt{\frac{P_H}{{\rho }_H}\times \frac{{\rho }_{\text{air}}}{P_{\text{air}}}}=\sqrt{\frac{{\rho }_{\text{air}}}{{\rho }_H}}$
(as $P_{\text{air}}=P_H)$
(Here,${\gamma }_{air}={\gamma }_H$as hydrogen is a diatomic gas and air is mainly a mixture of diatomic gases.)
$\Rightarrow v_H=v_{\text{air}}\times \sqrt{\frac{{\rho }_{\text{air}}}{{\rho }_H}}=332\times \sqrt{\frac{16}{1}}=1328\text{m/s}$