Velocity of Sound in Gas (Newton’s formula)According to Newton, when sound waves PROPAGATE in air, compression and rarefaction are formed. He assumed that the process is very slow and the HEAT produced during compression is given to surrounding and heat loss during compression is gained from surrounding. So the temperature remains constant and sound waves propagate through an isothermal process.Derivation of Newton's FormulaAccording to gas law (Boyle's law),PV = constantwhere, P = pressure V = volume of air Differentiating above equation, we getpdv+vdp=0pdv=-vdpp=vdp/dvp=dp/-(dv/v)p=Bwhere, B is the bulk modulus of the air.If B is the bulk modulus of the air, v is velocity and ρ is the density, then, velocity is given by:v=√(b/p)v=√p/¶ Relationship of velocity or air with bulk modulus and density This is the required expression for velocity of sound in air.Calculation of Velocity of airNow, the velocity of sound in air using Newton's formula at NTP (NORMAL Temperature and Pressure) is given by:Pressure (P)= 1.1013 * 105 N/m2Density of air (ρ) = 1.293 kg/m3v=√(1.013*10^5)/1.023=280m/sCalculation of velocity of sound in air with Newton's formula