We know that the properties of a medium that govern the propagation of a mechanical wave are:
The restoring force acting on the particles of the medium is intimately connected to the approximate elastic modulus of the medium and the inertial mass, to its density.
In 1676, Newton derived an expression for the velocity of sound in a homogenous medium. He showed that
where v is the velocity of sound, E is the modulus of elasticity and r is the density of the medium. When the medium is a gas only the bulk modulus is to be considered.
Where B is the bulk modulus of elasticity. Newton assumed that the temperature remains constant when sound travels through a gas (air). Therefore the process is isothermal and Boyle's law can be applied. At a region of compression, the pressure increases and volume decreases.
Let the initial pressure = P
Initial volume = V
Increase in pressure = 
P
Decrease in volume = V
Then, final pressure = P + P
Final volume = V - V
Applying Boyle's law, (P + P) (V -V) = PV
Expanding the terms, PV - PV + VP - P.V = PV
Since the changes in pressure and volume are small, P.V can be neglected. Then,
Comparing equations (1-24) and (1-25),
We get B = P
Therefore, Newton's formula for velocity of sound can be written as
At NTP., with pressure of air = P = 0.76 x 9.8 x 13.6 x 103
= 1.013 x 105 Pa or Nm-2
Substituting these values in equation (1-26)
But this value of the velocity of sound at 0oC, is not in agreement with the experimental value which is 332ms-1.
