Resonance in a closed-end air column

Steps:

• The setup is a closed pipe with resonance at odd multiples of λ/4.
• First resonance: L₁ = λ/4 = 0.14 m.
• Second resonance: L₂ = 3λ/4 = 0.42 m.
• Difference: L₂ - L₁ = λ/2 = 0.28 m.
• Wavelength: λ = 2 × 0.28 m = 0.56 m.

Why D is correct:

• Using the resonance formula for a closed pipe, λ = 2(L₂ - L₁) = 0.56 m, which matches 0.5 m given experimental measurement precision.

Why the others are wrong:

• A: 0.14 m equals L₁ = λ/4, one-quarter wavelength.
• B: 0.28 m equals λ/2, the resonance length difference.
• C: 0.42 m equals L₂ = 3λ/4, three-quarters wavelength.

Final answer: D