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Fundamental frequency of closed organ pipe, v_c = V/4ℓ. Fundamental frequency of open organ pipe, v₀ = V/2ℓ₀. Second overtone frequency of open organ pipe = 3V/2ℓ₀. From question, v/4ℓ = 3V/2ℓ₀ ⇒ ℓ₀ = 6ℓ = 6 × 20 = 120 cm.

1. v_c = V/4ℓ
2. v₀ = V/2ℓ₀
3. Second overtone frequency = 3V/2ℓ₀
4. ℓ₀ = 6ℓ = 120 cm

Correct answer: ℓ₀ = 6ℓ = 120 cm

Solution

The calculation provided in the question shows that ℓ₀ = 6ℓ = 6 × 20 = 120 cm, which matches option D. The other options are definitions or given data, not the final result.

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