Sound travels in air as a longitudinal wave. The wave motion is therefore, accompanied by compressions and rarefaction& At compressions the temperature of air rises and at rarefactions, due to expansion, the temperature decreases. The above discrepancy observed was explained by Laplace in 1816.

Air is a very poor conductor of heat. Hence at a compression, air cannot lose heat due to radiation and conduction. At a rarefaction it cannot gain heat, during the small interval of time. As a result, the temperature throughout the medium does not remain constant.

Laplace suggested that sound waves travel in air under adiabatic condition and not under isothermal condition.

For an adiabatic change, the relation between pressure and volume is given by

**P V ^{γ} = constant**

Where γ = (C_{P}/C_{V}) is the ratio of two specific heat capacities of the gas.

Differentiating,

P^{γ} = -dP/(dV/V) = k

So, P^{γ} = k (Volume elasticity)

Therefore under adiabatic condition

velocity of sound, **v = √(k/ρ) = √(Pγ/ρ)**

This is Laplace’s corrected formula.