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Question
Answer briefly.
What is the effect of humidity of air on velocity of sound?
Solution
- Let vm and vd be the velocities of sound in moist air and dry air respectively.
∴ `"v"_"m" = sqrt((gamma"P")/(rho_"m"))` and `"v"_"d" = sqrt((gamma"P")/(rho_"d"))`
∴ `"v"_"m"/"v"_"d" = sqrt((gamma"P")/(rho_"m")) xx sqrt((rho_"d")/(gamma"P"))`
= `sqrt(gamma/gamma xx (rho_"d")/(rho_"m")) = sqrt((rho_"d")/(rho_"m"))` - Humid air contains a large proportion of water vapour. Density of water vapour at 0 °C is 0.81 kg/m3 while that of dry air at 0 °C is 1.29 kg/m3. So, the density ρm of moist air is less than the density ρd of dry air i.e.,ρm < ρd.
- Thus, `"v"_"m"/"v"_"d"` > 1
∴ vm > vd - Hence, sound travels faster in moist air than in dry air. It means that the velocity of sound increases with an increase in moistness (humidity) of air.
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