Scientist Laplace first pointed out that the propagation of sound waves through a gaseous medium takes place under adiabatic conditions and not under isothermal conditions as assumed by Newton. According to Laplace’s assumption, compressions and rarefactions occur so quickly that the temperature of a gas can’t remain constant.
On the other hand, heat exchange doesn’t take place among different portions of the gas during that small time interval. As a result, the temperature of gaseous layers increases and decreases during the propagation of sound – The process is essentially adiabatic.
Now, the relation between pressure (p) and volume (V) of a gas under adiabatic conditions is given by
pVγ = constant
γ = moler specific heat of the gas at constant pressure (Cp) / moler specific heat of the gas at constant volume (Cv)