The speed of sound in oxygen ( O 2) at a certain temperature is 460 ms -1. The speed of sound in helium ( He ) at the same temperature will be (assume both gases to be ideal).

Question

The speed of sound in oxygen ( O 2) at a certain temperature is 460 ms -1. The speed of sound in helium ( He ) at the same temperature will be (assume both gases to be ideal). (A) 1421 ms -1 (B) 500 ms -1 (C) 650 ms -1 (D) 330 ms -1

Tardigrade Admin · Accepted Answer

The speed of sound in a gas is given by

v = \frac{γ RT}{M}

∴ \frac{v _{O_{2}}}{v _{He}} = \frac{γ _{O_{2}}}{M _{O_{2}}} \times \frac{M _{He}}{γ _{He}} = \frac{1.4}{32} \times \frac{4}{1.67} = 0.3237

∴ v_{He} = \frac{v _{O_{2}}}{0.3237} = \frac{460}{0.3237} = 1421 m / s

Q. The speed of sound in oxygen $(O_{2})$ at a certain temperature is $460 m s^{- 1}$ . The speed of sound in helium $(He)$ at the same temperature will be (assume both gases to be ideal).

$1421 m s^{- 1}$

$500 m s^{- 1}$

$650 m s^{- 1}$

$330 m s^{- 1}$

The speed of sound in a gas is given by $v = \frac{γ RT}{M}$
$∴ \frac{v _{O_{2}}}{v _{He}} = \frac{γ _{O_{2}}}{M _{O_{2}}} \times \frac{M _{He}}{γ _{He}} = \frac{1.4}{32} \times \frac{4}{1.67} = 0.3237$
$∴ v_{He} = \frac{v _{O_{2}}}{0.3237} = \frac{460}{0.3237} = 1421 m / s$

Q. The speed of sound in oxygen (O2​) at a certain temperature is 460ms−1. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal).

1421ms−1

500ms−1

650ms−1

330ms−1