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.

Explanation

(i) The speed of sound in a gas given by, `v=sqrt((gammaP)/(rho))`
At constant temperautre, `PV=`constant,`(Pm)/(rho)=`cosntant
Since m is constant, so `(P)/(rho)`=constant
ie., when pressure changes density also changes in the same ratio so that the factor `(P)/(rho)` remains unchanged. hence the pressure has no effect on the speed of sound a gas for a given temperature.
(ii) We know that
`PV=nRT" " or P=(nRT)/(V)`
also `v=sqrt((gammaP)/(rho))=sqrt((gammanRT)/(rhoV))=sqrt((gammaRT)/(M))`
Where M=molecular weight of the gas
As `gamma,R` and M are constant, so `vpropsqrt(T)`,
i.e., velocity of sound in a gas is directly proportional to the square root of its temperature, hence we conclude that the velocity fo sound in air increases with increase in temperature.
(iii) As `v=sqrt((gammaP)/(rho))` ,i.e., `vprop(1)/(sqrt(rho))`
The density of water vapours is less than that of dry air. Since the speed of sound is inversely proportional to the square root of density, so speed of sound increases with increase in humidity.