Question

give newton's formula for the velocity of sound in air and state its assumptions.

Answer 1

Assumption: 1) the change in pressure and volume of gas, when sound waves are propagated through a gas in the form of compression, are isothermal in nature. 2) The amount of heat produced during compression is lost to the surrounding and similarly the amount of heat lost during rarefaction is taken from surrounding.

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Answer 2

The formula for velocity of sound in air is given by :- v = √p/ρ where p is the pressure and ρ is the density.

Explanation:

Velocity of longitudinal wave in elastic media is

v = √E/ρ where E is the elasticity and ρ is the density..

Newton's assumed that sound wave travel in air under isothermal condition.

Therefore v = $\sqrt{\frac{E_{iso} }{p} }$

For isothermal process PV = constant, on differentiating , we get

PdV + VdP = 0

$\frac{dP}{dV}V = - P$

Now volume density is,

E = $-V\frac{dP}{dV}$

Therefore $E_{iso}$ = ρ

Thus v = √P/ρ

At NTP , the density of air is 1.293kg/m³.

Therefore the velocity of air is given by

v = √P/ρ = $\sqrt{\frac{1.01x10^{5} }{1.293} }$  = 280m/s

The value is appoximately 16% less than the experimental value is 332m/s .

Newton's Assumption of isothermal propagation of sound  through gas was wrong and Laplace's corrected it as an adiabatic change