Use the formula v = √(rP/ρ) to explain why the speed of sound in a

1.	Use the formula v = √(rP/ρ) to explain why the speed of sound in air 1. Is Independent of pressure, 2. Increases with temperature, 3. Increases with humidity.
Answer» Given v = √(rP/ρ)…...(1) According ideal gas law, P = (ρRT/M),where ρ is the density, T is the temperature, M is the Molecular mass of the gas; R – universal gas constant. Substituting for P in (1) we get v =√(rRT/M) This shows that v is 1. Independent of pressure 2. Increases with temperature i.e. v ∝ √T 3. We know that the molecular mass of water (18) is less than that of N₂ (28) and O₂ (32). therefore as humidity increases, the effective molecular mass of air decreases and hence velocity increases.

Use the formula v = √(rP/ρ) to explain why the speed of sound in air 1. Is Independent of pressure, 2. Increases with temperature, 3. Increases with humidity.

Answer»

Given v = √(rP/ρ)…...(1)

According ideal gas law, P = (ρRT/M),where

ρ is the density, T is the temperature, M is the Molecular mass of the gas;

R – universal gas constant.

Substituting for P in (1) we get

v =√(rRT/M)

This shows that v is

1. Independent of pressure

2. Increases with temperature i.e. v ∝ √T

3. We know that the molecular mass of water (18) is less than that of N₂ (28) and O₂ (32). therefore as humidity increases, the effective molecular mass of air decreases and hence velocity increases.

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