Question

derive laplace correction formula

Answer 1

Newton assumed that when sound propagates through air, temperature remains constant (i.e. the process is isothermal).

So, bulk modulus of elasticity B = BT = p

(isothermal bulk modulus BT of a gas is equal to its pressure).

Therefore at NTP
p = 1.01 × 105 N/m2 and ρ = 1.3 kg/m3



= 279 m/s

The experimental value of v in air is 332 m/s at NTP. This discrepancy was removed by Laplace.

LAPLACE’S CORRECTION :

Laplace assumed that the propagation of sound in air is an adiabatic process not the isothermal.

B = Bs = γP [Adiabatic bulk modulus Bsof a gas = γP]

Where γ = Cp/Cv = 1.41 for air





Which is in agreement with the experimental value (332 m/s) thus,

We can conclude that sound waves propagate through gases adiabatically

Answer 2

$\textbf{Answer is in Attachment !!}$