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Newton's Formula for Velocity of Sound
Velocity Of sound in depends on the two factors:-
- Modulus of elasticity
- Density of medium.
By dimension method we can derive the formula for velocity of sound in any medium .
We get:-
where c is velocity of sound ,E is modulus of elasticity of the medium and p is density of medium.
Newton's expression
Newton assumed the propagation of sound wave in air as isothermal process.So he used isothermal equation of state. i.e.pv=constant
by differentiating both side,we get
-dP/(dv/v)=P
where dP is change in pressure
dv is change in volume
v is volume
P is pressure
since -dP/(dv/v) is numerically equal to modulus of elasticity.i.e bulk modulus of elasticity B for air.
Hence finally we come on the result that velocity of sound in air is given by
From this formula ,if we put the values of B and p,we get the value of velocity of sound nearly equal to 280m/s which is very smaller value than the actual value.So there must be some wrong in the formula.So Laplace corrected this formula and gave the name Laplace Correction.
See here Laplace Correction :
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Laplace's Correction To Newton's Formula
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