Question
What correction was applied by Laplace to remove the discrepancy given by Newton's formula and why?
Solution
Laplace correction:
Laplace suggested that sound waves travel through air under adiabatic conditions and not under isothermal conditions because air is a bad conductor of heat. Also, compression and rarefaction of air takes place rapidly.
Therefore according to Laplace, the velocity of sound in air is,
For adiabatic changes,
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Thus,
Since air is diatomic, therefore γ = 1.4.
Substituting the values of γ, P and ρ, we get
This result agrees with the experimental value.
Laplace suggested that sound waves travel through air under adiabatic conditions and not under isothermal conditions because air is a bad conductor of heat. Also, compression and rarefaction of air takes place rapidly.
Therefore according to Laplace, the velocity of sound in air is,
For adiabatic changes,
∴
Thus,
Since air is diatomic, therefore γ = 1.4.
Substituting the values of γ, P and ρ, we get
This result agrees with the experimental value.
