According to Newton the change in pressure & volume in air is an isothermal process. Therefore he calculated,v =√(p/p) on substituting the require value he found, the velocity of sound was not in close agreement with the observation value. Then Laplace pointed out the error in Newton’s formula. According to Laplace the change in pressure and volume is an adiabatic process. So he calculated the value of sound as, v =√(yr/p) on putting require value he found velocity of sound as 332m/s very closed to observed theory.
