Question

find the Newton's formula for velocity of sound​

Answer 1

Answer:

Newton's formula for velocity of sound in gas is: v=ρP , where P is pressure & ρ is density of gas.

Answer 2

$\huge \fbox \red{Answer}$

According to Boyle’s law

PV = Constant

Where,

P is pressure

V is the volume of gas.

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On differentiating above equation we get-

PdV + VdP = 0

⇒ PdV = -VdP

$P = - \frac{VdP}{dV} = \frac{dP}{ - ( \frac{dV}{V}) }$

⇒ P = B

Where, B = $\frac{dP}{ - ( \frac{dV}{V}) }$ is bulk modulus of air.

The velocity of the sound wave can be written as-

$v = \sqrt{ \frac{B}{ρ} }$

Thus substituting B = P we get -

$v = \sqrt{ \frac{P}{ρ} }$