## Saturday, July 12, 2008

### Newton’s formula for speed of sound in a gas

Newton’s formula for speed of sound in a gas

v = √(P/ρ)

The density of air at temperature 0°C and pressure 76 cm of mercury column is ρ = 1.293 kg/m³

So P = .76m*(13.6*10^3 kg/ m³)*(9.8 m/s²) = 101292.8

Hence P/ ρ = 78339.37
√(P/ρ) = 279.8917 m/s

The velocity of sound in air comes as 280 m/s.

But the measured value of speed of sound in air is 332 m/s

Laplace's Correction

Laplace suggested a correction. With Laplace’s correction the formula is

v = √( γ P/ρ)

where γ = Cp/Cv (Cp and Cv are molar heat capacities at constant pressure and constant volume respectively)
With this new formula the value comes out to be 331.1723 closer to 332 m/s.