Write the Newton's formula for speed of a wave in air. Explain Laplace correction in Newton's formula.
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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 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
hope it helps
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
hope it helps
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