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

Step-by-step solution

For Oxygen, Molar mass, M₁=32 Heat capacity ratio at constant pressure to that at constant volume, ₁=C_p / C_V=7 / 5 [for diatomic gas] Speed of sound, v₁=460 ~m / s For Helium, Molar mass, M₂=4 Heat capacity ratio (C_p / C_V ) , ₂= 5 3 [for monoatomic gas] Let speed of sound =v₂ Using the expression of speed of sound in an ideal gas at certain temperature (T) is array rlrl & v= R T M & v₁ & = ₁ R T M₁ ...(i) and & v₂ & = ₂ R T M₂ ...(ii) array Dividing Eq. (i) by Eq. (ii), we get v₁ v₂ = ₁ R T M₁ M₂ ₂ R T = ₁ ₂ M₂