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Please explain the differences between mode and motion (as in translation/rotation/vibration) How is vibrational motions are...

Please explain the differences between mode and motion (as in translation/rotation/vibration)

How is vibrational motions are related to speed of sound?

Can you explain it with this equation,

heat capacity ratio = Cp/Cv = (molar mass x speed of sound^2) / (RT)

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