Question

WHAT WAS WRONG ASSUMPTION MADE BY NEWTON TO OBTAIN THE SPEED OF THE SOUND IN AIR?HOW DID LAPLACE CORRECT IT?WRITE NEWTON'S AND LAPLACE'S FORMULA FOR SPEED OF SOUND IN AIR.

Answer 1

Dear Student,
According to Newton The compression and rarefaction of sound waves are slow, because of which Heat is constantly gained and lost during the progression which maintains the temperature of air constant and hence assumed isothermal process.
where bulk modulus B=P of gas at NTP

According to Laplace The compression and rarefaction of sound waves are fast, because of which Heat is not lost or gained during the progression and assumed an adiabatic condition. Where bulk modulus B=γP
​Velocity Of Sound

$$\begin{gathered} \nu =\sqrt{\frac{B}{\rho }} \\ P=1.01\times {10}^5\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$m^2$}\right. \\ \rho =1.293\raisebox{1ex}{$Kg$}\!\left/ \!\raisebox{-1ex}{$m^3$}\right. \\ {\rm Y}=1.4foradiabatic \end{gathered}$$

Newton's Speed of Sound=280 m/s
Laplace's​ Speed of Sound=332 m/s


Good Luck...!!!