Question

At the room temperature velocity of sound in ${O_2}$ gas is $V$. Then in mixture of ${H_2}$ and ${O_2}$ gas the speed of sound at same temperature
A. Will be less than $V$
B. Will be more than $V$
C. Will be equal to $V$
D. Nothing can be said

Answer 1

In order to solve this question we need to understand RMS speed of sound and its dependency on medium. RMS speed is defined as the root mean square speed of sound. It is the speed by which sound moves in medium on an average. It is directly proportional to the root of temperature and inversely proportional to the molar mass of gas in which sound travels.

Complete step by step answer:
As stated above root mean square speed of sound is inversely proportional to molar mass of gas.Root mean square speed of sound is given by
$v = \sqrt {\dfrac{{\gamma RT}}{M}}$
Where $M$ is molar mass of gas.
Since Temperature is same so speed is inversely proportional to molar mass which can be written as $v = \dfrac{k}{{\sqrt M }}$
Since Molar mass of mixture of ${H_2}$ and ${O_2}$ gas is greater than molar mass of ${O_2}$ gas alone so speed of mixture would be less than speed of ${O_2}$ gas.

So the correct option is A.

Note: It should be remembered that classical gas follows Maxwell Boltzmann statistics so sound travels in such a medium with root mean square speed of classical gas. Also sound waves are longitudinal waves and it is considered to be motion of compression and rarefaction. Also $\gamma$ in expression of speed of sound is known as isentropic exponent.