Question
Use the formula v = 
to explain why the speed of sound in air:
(b) increases with temperature,
Solution
Take the relation,
v = √γP/ρ ...(i)
For one mole of any ideal gas, the equation can be written as:
PV = RT
P = RT/V ...(ii)
Substituting equation (ii) in equation (i), we get:
v = √γRT/Vρ = √γRT/M ...(iii)
where,
mass, M = ρV is a constant
γ and R are also constants.
We conclude from equation (iii) that v ∝ √T
Hence, the speed of sound in a gas is directly proportional to the square root of the temperature of the gaseous medium, i.e., the speed of the sound increases with an increase in the temperature of the gaseous medium and vice versa.
v = √γP/ρ ...(i)
For one mole of any ideal gas, the equation can be written as:
PV = RT
P = RT/V ...(ii)
Substituting equation (ii) in equation (i), we get:
v = √γRT/Vρ = √γRT/M ...(iii)
where,
mass, M = ρV is a constant
γ and R are also constants.
We conclude from equation (iii) that v ∝ √T
Hence, the speed of sound in a gas is directly proportional to the square root of the temperature of the gaseous medium, i.e., the speed of the sound increases with an increase in the temperature of the gaseous medium and vice versa.
