Question

The ratio of velocity of sound in hydrogen and oxygen at STP is :

• A. $16:1$
• B. $8:1$
• C. $4:1$
• D. $2:1$

Answer 1

Answer: (C)

$4:1$

The velocity of sound in a gas is given by $v=\sqrt{\gamma RT/M}$ ,

where $\gamma =$ ratio of specific heats at constant pressure and temperature,

$T=$ absolute temperature of the gas,

$M=$ molecular mass of the gas,

$R=$ gas constant,

At STP, temperature $T$ of both the given gases will be same, and as both the gases are diatomic so $\gamma$ is also same for both gases.

Now, molecular mass of Hydrogen $M_H=2gmo{l}^{-1}$,

Molecular mass of Oxygen $M_O=32gmo{l}^{-1}$ ,

Hence , velocity of sound in Hydrogen $v_H=\sqrt{\gamma RT/2}$

Velocity of sound in Oxygen $v_O=\sqrt{\gamma RT/32}$ ,

Therefore, $v_O/v_H=\sqrt{32/2}=4/1$ i.e. $v_O:v_H=1:4$

$⟹$ $v_O:v_H=4:1$