Derive newton's formula for velocity of …
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Posted by Sai Syran 8 years, 9 months ago
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Shweta Gulati 8 years, 9 months ago
According to Newton, when sound waves propagate in air, compression and rarefaction are formed. He assumed that the process is very slow and the heat produced during compression is given to surrounding and heat loss during compression is gained from surrounding. So the temperature remains constant and sound waves propagate through an isothermal process.
According to gas law (<a href="https://en.wikipedia.org/wiki/Boyle%27s_law">Boyle's law</a>),
<pre> PV = constant where, P = pressure V = volume of air </pre>Differentiating above equation, we get
where, B is the bulk modulus of the air.
If B is the bulk modulus of the air, v is velocity and ρ is the density, then, velocity is given by:
This is the required expression for velocity of sound in air.
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