1.

Use the formula v = √{γp/ρ} to explain why the speed of sound in air(i) is independent of pressure,(ii) increases with temperature,(iii) increases with humidity.

Answer»

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.


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