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Question
Speed of sound wave in air ______.
Options
is independent of temperature.
increases with pressure.
increases with increase in humidity.
decreases with increase in humidity.
Solution
Speed of sound wave in air increases with increase in humidity.
Explanation:
We know that the speed of sound in air is given by
`v = sqrt((γP)/ρ)`, For air γ and P are constants.
`v ∝ 1/sqrt(ρ)` where ρ is the density of air.
⇒ `v_2/v_1 = sqrt(ρ_2/ρ_1)`
Where ρ1 is the density of dry air and ρ2 is the density of moist air. Due to the presence of moisture, the density of air decreases.
As `ρ_2 < ρ_1 = v_2/v_1 > 1`
⇒ `v_2 > v_1`
Hence, the speed of sound wave in air increase with increase in humidity.
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