First slide

Travelling wave

Question

The ratio of the velocity of sound in hydrogen $(γ = \frac{7}{5})$ to that in helium $(γ = \frac{5}{3})$ at the same temperature is

Moderate

A

$\sqrt{\frac{5}{42}}$
B

$\sqrt{\frac{5}{21}}$
C

$\frac{\sqrt{42}}{5}$
D

$\frac{\sqrt{21}}{5}$

Solution

Velocity of sound in gas
$v = \sqrt{\frac{γRT}{M}}$
where the symbols have their usual meanings.
At the same temperature,
$v \propto \sqrt{\frac{γ}{M}} ∴ \frac{v_{H_{2}}}{v_{He}} = \sqrt{\frac{γ_{H_{2}}}{γ_{He}} \times \frac{M_{He}}{M_{H_{2}}}} = \sqrt{\frac{7}{5} \times \frac{3}{5} \times \frac{4}{2}} = \frac{\sqrt{42}}{5}$

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