Derive the newtons formula to find the speed of a longitudinal wave in an ideal gas. What is the laplace correction in obtaining the speed of sound in air?
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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 Bs of 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
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