First slide

Travelling wave

Question

The speed of sound in oxygen $(O_{2})$ at certain temperature is $460 m / \sec$ . The speed of sound in Helium (He) at same temperature will be (assumed both gases to be ideal)

Moderate

A

460 m/s
B

500 m/s
C

650 m/s
D

1420 m/s

Solution

$S p e e d o f s o u n d i n g a s V = \sqrt{\frac{γ R T}{m}} ∴ \frac{V_{1}}{V_{2}} = \sqrt{\frac{γ_{1}}{γ_{2}} \times \frac{m_{2}}{m_{1}}} = \sqrt{\frac{\frac{7}{5} \times 4}{\frac{5}{3} \times 32}} \Rightarrow \frac{460}{V_{2}} = \sqrt{\frac{21}{25 \times 8}} \Rightarrow V_{2} = \frac{460 \times 5 \times 2 \sqrt{2}}{\sqrt{21}} = 1420 m / \sec$

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