If ℓ₁ and ℓ₂ are the air-column lengths for the first and second resonances of a resonance tube with the same tuning fork, find the distance of the displacement antinode from the open end.
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If ℓ₁ and ℓ₂ are the air-column lengths for the first and second resonances of a resonance tube with the same tuning fork, find the distance of the displacement antinode from the open end.

G1 Physics · Accepted Answer

Step 1: For a resonance tube, first two effective lengths are ℓ₁+e=λ/4 and ℓ₂+e=3λ/4. Step 2: Subtract to get λ/2=ℓ₂−ℓ₁. Solving for end correction gives e=(ℓ₂−3ℓ₁)/2. The displacement antinode lies a distance e beyond the open end. Final: C.