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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.
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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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