Consider a gas with molar mass M . If the sound at frequency f is introduced to a tube of this gas at temperature T then an internal acoustic standing wave is set up with nodes separated by L . The adiabatic constant γ = C p C v is

Question

Consider a gas with molar mass M . If the sound at frequency f is introduced to a tube of this gas at temperature T then an internal acoustic standing wave is set up with nodes separated by L . The adiabatic constant γ = C p C v is, M f 2 L 2 R T, M f 2 L 2 4 R T, 4 M f 2 L 2 R T, 3 M f 2 L 2 2 R T

MARKS App · Accepted Answer

Recall the formula of the fundamental frequency of the standing wave, f = v 2 L , and the formula of sound waves in terms of absolute temperature and molecular mass, v = 3 R T M , ⇒ f = γ R T M 2 L ⇒ f 2 × 4 L 2 = γ R T M ⇒ γ = f 2 × 4 L 2 M R T

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