Question

Write newton-laplace equation for the speed sound in air.Name two factors which affect the speed of sound in air?​

Answer 1

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The speed of sound in air depends on the type of gas and the temperature of the gas. On Earth, the atmosphere is composed of mostly diatomic nitrogen and oxygen, and the temperature depends on the altitude in a rather complex way.

Answer 2

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Laplace Correction

The velocity of sound is given by v=Bρ−−√ and has an experimental value of 332 m/s.

Newtons formula for the speed of sound

Newton worked on the propagation of sound waves through the air. He assumed that this process of propagation is isothermal. Absorption and release of heat during compression and rarefaction will be balanced, thus, the temperature remains constant throughout the process.

According to Boyle’s law

PV = Constant

Where,

P is pressure

V is the volume of gas.

On differentiating above equation we get-

PdV+VdP=0

⇒ PdV = -VdP

⇒P=−VdPdV=dP−(dVV)

⇒ P = B

Where, B=dP−(dVV) is bulk modulus of air.

The velocity of the sound wave can be written as –

v=Bρ−−√

Thus substituting B =P we get-

v=Pρ−−√

Speed of sound in air

At Normal Temperature and Pressure, the velocity of sound in air is given by –

v=Pρ−−√

Where atmospheric pressure P = 1.1013×105 N/m2

The density of air ()= 1.293 kg/m3

v=Pρ−−√=1.013×1051.293−−−−−−−√=280m/s

The value got here does not match with the experimental value. That is 332 m/s. Which implies that some correction should be done to Newton’s equation.