Question

How Laplace corrected Newton's formula for the speed of sound in
a gas
Derive an expression for it.
​

Answer 1

douught is dought ..............m

Answer 2

Explanation :-

Laplace Correction for Newton’s Formula

He corrected the Newtons formula by assuming that, there is no heat exchange takes place as the compression and rarefaction takes place very fast. Thus, the temperature does not remain constant and the propagation of the sound wave in air is an adiabatic process.

For an adiabatic process

PV = Constant

Where,

is adiabatic index γ=CpCv

Cp specific heat for constant pressure

Cv specific heat for constant volume.

Differentiating both the sides we get-

VγdP+PγVγ−1dV=0

Dividing both the sides by V-1

VdP+PγVdV=0 Pγ=−dP(dVV)=B

The velocity of sound is given by

v=Bρ−−√

Substituting B= P in above equation we get-

Velocity of sound formula

v=γPρ−−−√

Velocity of sound

Calculate the velocity of sound wave using Laplace correction to Newton’s formula at Normal Temperature and Pressure.

Velocity of the sound formula is given by-

v=γPρ−−−√

Where,

Adiabatic index – 1.4

Where atmospheric pressure P = 1.1013×105 N/m2

The density of air ()= 1.293 kg/m3

Substituting the values in the equation we get-

v=γPρ−−−√=1.4×1.013×1051.293−−−−−−−−−√=332m/s

Which has a very good match with the experimental value.

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