Question

Explain Newtons formula for velocity
of sound. What is its limitation?​

Answer 1

Explanation:

newton considered the motion of sound waves, because of isothermal compression & rarefaction.

he used the formula, for calculating speed of sound

C = √ (R*T)

at NTP T =293 °k

& gas constant for air R = 287 J/kg°k

we get the value

C = √(287*293) = 289.98 m/s

which is 15.5 % less than actual value of speed of sound.

Laplace made the correction in Newtons formula, by assuming motion of sound waves by adiabatic compression & rarefaction.

so we have to multiply by factor gamma, which is ratio of specific heat ratio, also called as adiabatic index. its value for air is 1.4. if we multiply by 1.4, we get

C = √(1.4*287*293)

C = 343.11 m/s

which is most exact value of speed of sound, at NTP.