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