First slide

Travelling wave

Question

The speed of sound in a gas is V and the root mean square speed of gas molecules is $v_{r m s}$ . If the ratio of the specific heats of gas $γ = 1.5$ then ratio $v / v r m s$ is

Moderate

A

1:3
B

1:4
C

$1 : \sqrt{2}$
D

1:2

Solution

$R o o t M e a n S q u a r e V e l o c i t y : V_{r m s} = \sqrt{3 \frac{P}{ρ}} S p e e d o f s o u n d i n a g a s : V = \sqrt{γ \frac{P}{ρ}} ∴ \frac{V}{V r m s} = \sqrt{\frac{γ}{3}} = \sqrt{\frac{1.5}{3}} = \frac{1}{\sqrt{2}}$

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