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Pressure P 11013 105 Nm2 Density of air ρ 1293 kgm3 Calculation of velocity of sound in air with Newtons formula.

Newton's formula for velocity of sound. E coefficient of elasticity of medium. Newtons FormulaNewton assumed that when sound waves propagate through gas compression and rarefaction are produced in the medium. Newtons formula for the velocity of sound in a gas was the following.

V pρ. Velocity of Sound in Gas. So Laplace introduced a correction term Y into the formula where Y is the Youngs modulus of the medium.

At NTP the density of air is 1293 kgm 3. The vibration of the temperature in the region of compression and rarefaction are negligible or an isothermal process Boyles law holds true. The changes of these compressions and rarefaction take place at a slow rate.

Now the velocity of sound in air using Newtons formula at NTP Normal Temperature and Pressure is given by. This is possible only in an elastic medium. Newton assumed that sound wave travels in air under isothermal condition.

Relationship of velocity or air with bulk modulus and density This is the required expression for velocity of sound in air. After 100 years Laplace corrected the Newtons assumption for velocity of sound. Newtons formula for velocity is wrong as it gives value 280 ms which is wrong because velocity of sound calculated by modern experiment is 332 ms.

Laplace Correction of Newtons Formula Laplace provided a correction for Newtons formula. This is much lower than the experimental value of 332 ms. Where E is elasticity and ρ is density of media.

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