Newton assumed that sound waves travel through air under isothermal conditions (i.e) temperature of the medium remains constant.
The change in pressure and volume obeys Boyle’s law.
PV = constant
Differentiating, P.dV + V.dP = 0
dV = -V dP
So, P = -dp / (dV/V)
P = k (volume elasticity), therefore under isothermal condition, P = k
then, V = √(k/ρ) = √(P/ρ)
where P is the pressure of air and ρ is the density of air. The above equation is known as Newton’s formula for the velocity of sound waves in a gas.
At NTP, P = 76 cm of mercury
= (0.76 x 13.6 x 108 x 9.8) N m-2
ρ = 1.293 kg m-3.
Velocity of sound in air at NTP is;
V = √[(10.76 x13.6 x108 x 9.8) / 1.293]
= 280 ms-1
The experimental value for the velocity of sound in air is 332 m s-1. But the theoretical value of 280 m s-1 is 15% less than the experimental value. This discrepancy could not be explained by Newton’s formula.