Question
Derive Newton's formula for the velocity of sound in air.
Solution
Velocity of longitudinal wave in elastic media is,
where E is elasticity and ρ is density of media.
Newton assumed that sound wave travels in air under isothermal condition.
Therefore,
For isothermal process,
On differentiating, we get
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Now volume elasticity is,
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Thus,
At NTP, the density of air is 1.293 kg/m3.
∴
Velocity of sound in air is given by,
This value is approximately 16% less than the experimental value 332 m/s.
where E is elasticity and ρ is density of media.
Newton assumed that sound wave travels in air under isothermal condition.
Therefore,
For isothermal process,
On differentiating, we get
Now volume elasticity is,
∴
Thus,
At NTP, the density of air is 1.293 kg/m3.
∴
Velocity of sound in air is given by,
This value is approximately 16% less than the experimental value 332 m/s.
