Derive newton\'s formula for velocity of sound in air

1.	Derive newton\'s formula for velocity of sound in air
Answer» According to Newton, when sound waves propagate in air, compression\xa0and\xa0rarefaction\xa0are 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 (Boyle\'s law), PV = constantwhere, P = pressure V = volume of air Differentiating above equation, we getwhere,\xa0B\xa0is the bulk modulus of the air.If\xa0B\xa0is the bulk modulus of the air,\xa0v\xa0is velocity and\xa0ρ\xa0is the density, then, velocity is given by:This is the required expression for velocity of sound in air.

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