Question

derive Newton's formula for speed of sound in ideal gas what is Laplace correction​

Answer 1

Explanation:

A correction to the calculation of the speed of sound in a gas. Newton assumed that the pressure–volume changes that occur when a sound wave travels through the gas are isothermal. Laplace was subsequently able to obtain agreement between theory and experiment by assuming that pressure–volume changes are adiabatic.

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Answer 2

Newton's formula for speed of sound in ideal gas and Laplace correction​

Explanation:

• The general formula for speed of sound (longitudinal waves) is given by square root of the ratio of elasticity coefficient and density of the medium. For a fluid medium the elasticity coefficient becomes bulk modulus of medium.
• In case of gases specifically, the phenomenon of traveling of sound waves was proposed by Newton as isothermal process whereas later Laplace proposed it as an adiabatic process which comes to be correct. The bulk modulus of a gaseous medium for isothermal process can be proved to be equal to pressure of gaseous medium whereas the same for an adiabatic process can be proved to be equal to pressure of gas times the ratio of molar specific heats at constant pressure to molar specific heat at constant volume (gamma).
• When we put only pressure for bulk modulus in speed formula (proposed by Newton), the speed comes to be much less (around 280 m/s) than experimentally obtained value (around 330 m/s). On putting product of pressure and gamma in place of bulk modulus in speed formula (as proposed by Laplace) the speed comes to very close to experimental value.
• A correction to the calculation of the speed of sound in a gas. Newton assumed that the pressure–volume changes that occur when a sound wave travels through the gas are isothermal. Laplace was subsequently able to obtain agreement between theory and experiment by assuming that pressure–volume changes are adiabatic.

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