Question

The velocity of sound in oxygen is ________ than in helium.

Answer 1

Velocity of sound in a gas is given by ,

$v=\sqrt{\gamma RT/M}$

Hence , velocity of sound in helium is ,

$v_{He}=\sqrt{{\gamma }_{He}RT/M_{He}}$

And velocity of sound in oxygen is ,

$v_O=\sqrt{{\gamma }_{O}RT/M_O}$

Now , ${\gamma }_O=7/5,{\gamma }_{He}=5/3$ ,

Therefore , if temperature is constant

$\frac{v_O}{v_{He}}=\sqrt{\frac{{\gamma }_O{M}_O}{{\gamma }_{He}{M}_H}}$

or $\frac{v_O}{v_{He}}=\sqrt{\frac{\left(7/5\right)\times 32}{\left(3/2\right)\times 2}}=3.84$

The velocity of sound in oxygen is 3.84 than in helium .