Newtons Formula and Laplace Correction for the Speed of Sound

Velocity of Sound in Gas: Newton's Formula

Newton assumed that when sound waves propagate through gas, compression and rarefaction are produced in the medium. The changes of these compressions and rarefaction take place at a slow rate. Therefore, the process is isothermal. The equation of state for isothermal change is,

The negative sign indicates that as the pressure increases the volume decreases and vice versa. E is the isothermal bulk modulus of elasticity.

The experimental value for the velocity of sound in air at NTP was found to be 332 ms^-1. This difference between calculated and experimental value shows the need for some correction in Newton's formula. Later on, Laplace made a correction in Newton's formula now known as Laplace's correction.

Velocity of Sound in a Gas: Laplace's Correction

Laplace suggested that the change in pressure and volume of gas due to the passage of sound waves is not isothermal as assumed by Newton but it is adiabatic. Therefore, the appropriate modulus of elasticity is the adiabatic bulk modulus, i.e. E = K_adi: Thus, the velocity of sound in a gas is given by,