Discuss Newton's formula for velocity of sound in air.Point out the error and hence discuss Laplace's correction.Use Laplace formula to explain why the speed of a sound in air- 1) is dependent of pressure at constant temperature 2) increases with temperature PLEASE ANSWER THIS QUESTION FAST...
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Newtons' proposal:
v = √(B/ρ)
B = Bulk modulus of the gas = Pressure of the gas
ρ = density of the gas
Assumption:
Propagation of sound waves are isothermal. There is heat transfer to the surrounding at compressions and absorption from it at rarefactions.
But this formula deviated from experimental observations.
Laplace's correction:
v = √(γB/ρ) = √(γP/ρ)
where γ = ratio of specific heats of the gas at constant pressure and constant volume.
This formula takes into account the propagation of sound taking place as an adiabatic process. No heat transfers during the propagation to surroundings, as the velocity is high.
v = √(B/ρ)
B = Bulk modulus of the gas = Pressure of the gas
ρ = density of the gas
Assumption:
Propagation of sound waves are isothermal. There is heat transfer to the surrounding at compressions and absorption from it at rarefactions.
But this formula deviated from experimental observations.
Laplace's correction:
v = √(γB/ρ) = √(γP/ρ)
where γ = ratio of specific heats of the gas at constant pressure and constant volume.
This formula takes into account the propagation of sound taking place as an adiabatic process. No heat transfers during the propagation to surroundings, as the velocity is high.
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