Question

If cs be the velocity of sound in air and c be the rms velocity then

Answer 1

The velocity of sound in air is given by

Cs = √(γRT/M)

where γ is the degree of freedom

T = temperature

M = mass

According to the kinetic theory of gases,The rms velocity of sound is given by

C = √(3RT/M)

dividing both the equation we get

Cs/C = √γ/3

=> Cs = C√(γ/3)

Hence the required relation between speed of sound in air and rms speed is Cs = C√(γ/3)