Use the formula `upsilon = 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.

Explanation

(a)Effect of pressure `:`
The speed of sound in gases, `v= sqrt((gamma P)/( rho))` At constant temperature , PV =constant `P ( m )/( rho)` = constant `implies (P)/(rho)` = constant
If P increases , `rho ` also increases. Hence speed of sound in air is independent of pressure.
(b)Effect of temperature `:`
As PV `= n RT , P ( m)/( rho ) = ( m )/( M) RT `
`implies (P)/(rho) = (MT)/(M)`
` :. v = sqrt((RT)/( M))`
Since R, M are constant `v prop sqrt(T) `
`:.` Velocity of sound in air depends on temperature.
(c ) Effect of humidity `:`
As ` v = sqrt((gammaP)/( rho))` `: . v prop ( 1)/(sqrt((rho))`
As the density of water vapour is less than density of dry air at STP . So the presence of moisture in air decreases the density of air.Since the speed of sound is inversely proportional to the squuare root of density. So sound travels faster in moist air than dry air. Hence velocity of sound `V prop ` humidity.