Question

Why and what correction was applied by Laplace to Newton's formula for the speed of sound in air?​

Answer 1

Answer:

Laplace Correction for Newton's Formula

He corrected Newton's formula by assuming that, there is no heat exchange takes place as the compression and rarefaction takes place very fast. Thus, the temperature does not remain constant and the propagation of the sound wave in air is an adiabatic process.

Answer 2

Answer:

Laplace correction to the Newton's formula is that the sound in air travels by an adiabatic process not by isothermal process.

Explanation:

Newton' Formula

• The sound travels in air by the isothermal process.
• The formula for speed of sound in air is derived by ideal gas equation for isothermal process.
• The speed of sound in air according to Newton's formula is 280 m/s.

The Newton's formula is given by

v = √(P/ρ)

where v is the speed of sound in gas, P is the pressure of gas and ρ is the density of gas.

Laplace correction

• The sound travels in air very fast so exchage of heat can not take place and the temperature changes.
• The sound travels in air by adiabatic process.
• The formula for speed of sound in air is derived by ideal gas equation for adiabatic process.
• The speed of sound in air according to this formula is 331 m/s.

The new formula after Laplace correction is given by

v = √(γP/ρ)

where γ is the ratio of specific heat capacity, P is the pressure of gas and ρ is the density of air