The ratio of the speed of sound to the average speed of an air molecule at 300 ~K and 1 atmospheric pressure is close to-

Correct answer: (A) 1. fracV_sound V_av=√((γ kT)/m × (π M)/(8 kT))

Q76 / 90 · KVPY 2012 (SB/SX) · Physics

The ratio of the speed of sound to the average speed of an air molecule at $300 \mathrm{~K}$ and 1 atmospheric pressure is close to-

Correct answer
A
1
B
$\sqrt{1 / 300}$
C
$\sqrt{300}$
D
300

Solution

$\frac{\mathrm{V}_{\text {sound }}}{\mathrm{V}_{\mathrm{av}}}=\sqrt{\frac{\gamma \mathrm{kT}}{\mathrm{m}} \times \frac{\pi \mathrm{M}}{8 \mathrm{kT}}}$

Hence, the correct answer is option: 'A'.

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