Laplace’s correction - Propagation of Sound Waves

Laplace’s correction

In 1816, Laplace satisfactorily corrected this discrepancy by assuming that when the sound propagates through a medium, the particles oscillate very rapidly such that the compression and rarefaction occur very fast. Hence the exchange of heat produced due to compression and cooling effect due to rarefaction do not take place, because, air (medium) is a bad conductor of heat. Since, temperature is no longer considered as a constant here, sound propagation is an adiabatic process. By adiabatic considerations, the gas obeys Poisson’s law (not Boyle’s law as Newton assumed), which is

which is the ratio between specific heat at constant pressure and specific heat at constant volume.

Differentiating equation (11.23) on both the sides, we get

where, BA is the adiabatic bulk modulus of air. Now, substituting equation (11.24) in equation (11.16), the speed of sound in air is

Since air contains mainly, nitrogen, oxygen, hydrogen etc, (diatomic gas), we take γ= 1.47. Hence, speed of sound in air is vA = ( √1.4)(280 m s-1)= 331.30 m s-1, which is very much closer to experimental data.