Question

Find the ratio of speed of sound in hydrogen to the speed of sound in oxygen at $1270K$.

Answer 1

Velocity of sound in a gas is given by ,

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

Hence , velocity of sound in hydrogen is ,

$v_H=\sqrt{{\gamma }_{H}RT/M_H}$

And velocity of sound in oxygen is ,

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

Now , ${\gamma }_H={\gamma }_O$ ,because both are diatomic gases .

Therefore ,

$\frac{v_H}{v_O}=\sqrt{\frac{M_O}{M_H}}$

or $\frac{v_H}{v_O}=\sqrt{\frac{32}{2}}=\frac{4}{1}$

or $v_H:v_O=4:1$