The correct option is (A) n = 5, f2 = (5/4)f1.
Explanation:
Fundamental harmonic of open organ pipe is given by:
ℓ = (λ1 / 2) and V1 = (V / λ1) = (V / 2ℓ)
as tube vibrates in second harmonic, hence f1 = 2V1 = (2V / 2ℓ) = (V/ℓ)
if one end is close, it gives only odd harmonics & Fundamental frequency
= (V / 4ℓ)
other harmonics are (3V / 4ℓ), (5V / 4ℓ) etc.
One frequency starts increasing the first higher harmonic that is resonated is (3V / 4ℓ)
if n = 3, then f2 = (3V / 4ℓ) = (3/4)f1
However here is a snag. The frequency is increased from (V/ℓ) hence (3/4).
f1 is not greater than f1{f1 = (V/ℓ)}.
∴ (5/4)f1 is the answer
∴ Answer is n = 5 and f2 = 5 × (V / 4ℓ) = (5/4)f1