Newton’s formula for velocity of sound

Newton’s Calculation:

Sound wave propagates through a gaseous medium by the mechanism of formation of alternate layers of compression and rarefaction. Newton assumed that propagation of sound through a gaseous medium is an isothermal process.

Successive compression and rarefactions occur at such a rate that the temperature of the gaseous medium is constant during the propagation though the pressure and volume of the gaseous medium may change.

Air or any gas is a material medium. So the formula of velocity of sound is applicable to a gas. Since gas has no length or size, the bulk modulus is the only modulus of elasticity for it. Hence, if ρ is the density of the gas, k is the bulk modulus, then the velocity of sound through the gas is given by,

c = √(k/p)