First slide

Speed of wave

Question

In a mixture of gases, the average number of freedom per molecule is 6. The r.m.s. speed of the molecules of the gas is C. The velocity of sound in the gas is

Moderate

A

$C / \sqrt{2}$
B

$3 C / 4$
C

$2 C / 3$
D

$C / \sqrt{3}$

Solution

we know that $γ = 1 + (2 / f)$ where f =degrees of freedom

$∴ γ = 1 + \frac{2}{6} = \frac{8}{6} = \frac{4}{3} Further rrms = \sqrt{(\frac{3 RT}{M_{0}})} = C and v_{s} = \sqrt{(\frac{γRT}{M_{0}})} Dividing eq (2) by eq (1) we get \frac{V_{S}}{C} = \sqrt{(\frac{γ}{3})} = \sqrt{(\frac{4}{3 \times 3})} = \frac{2}{3} or v_{s} = 2 C / 3$

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