We are given that,
v = √{γp/ρ}
We know that pV = nRT
⇒ pV = m/M RT
where m is the total mass and M is the molecular mass of the gas.
p = m/M.RT/V = ρRT/M
⇒ p/ρ = RT/M
(a) For gas at constant temperature,
p/ρ = constant
As p increases, ρ also increases and vice versa. This implies that
v = √{γp/ρ} = const.
i.e., velocity is independent of pressure of the gas.
(a) Since p/ρ = RT/M
Therefore, v = √{γp/ρ} = √{γRT/M}
Clearly v α √T, i.e., Speed of sound in air increases with increase in temperature.
(c) Increase in humidity decreases the effective density of air.
Therefore, the velocity (v x 1/√ρ) increases.
