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Use the formula v= sqrt((gamma p)/(rho))...

Use the formula `v= sqrt((gamma p)/(rho))` to explain why the speed of sound in air
(a) is independent of pressure.
(b) increases with temperature.
(c ) increases with humidity

Text Solution

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Assume ideal gas law `p = (rho RT)/(M)`, where `rho` is the density, M is the molecular mass, and T is the temperature of the gas. This gives `v= sqrt((gamma RT)/(M))`. This shows that v is :
(a) Independent of pressure
(b) Increases as `sqrtT`
(c ) The molecular mass of water (18) is less than that of `N_(2) (28) and O_(2) (32)`
Therefore as humidity increases, the effective molecular mass of air decreases and hence v increases.
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