In a mixture of gases where the average number of degrees of freedom per molecule is 6 , the velocity of sound in the gas can be determined using the following relationships:
The root mean square (rms) speed
vrms is given by:
vrms=√‌The velocity of sound
v‌sound ‌ is given by:
v sound=√‌The ratio of the velocity of sound to the rms speed is:
‌=√‌Given that the degrees of freedom
f=6, we calculate the adiabatic index
γ as follows:
γ=1+‌=1+‌=‌Substituting
γ=‌ into the equation for the velocity of sound:
v sound=√‌vrms=‌vrmsTherefore, the velocity of sound in the gas is:
‌