Fundamental frequency in a closed tube Steps:

• For a tube closed at one end, the lowest frequency is the fundamental, where length L equals one-quarter wavelength: L = λ/4.
• Wavelength λ = v/f, with v = 340 m/s and f = 820 Hz, so λ = 340 / 820 ≈ 0.415 m.
• Thus, L = 0.415 / 4 ≈ 0.104 m = 10.4 cm.
• This matches option A (10 cm), accounting for rounding.

Why A is correct:

• It equals v/(4f) = 340/(4×820) ≈ 0.10 m, the exact formula for fundamental frequency in a closed pipe.

Why the others are wrong:

• B: 20 cm gives f = 340/(4×0.20) = 425 Hz, half the given frequency.
• C: 40 cm gives f = 340/(4×0.40) = 212.5 Hz, much lower than 820 Hz.
• D: 160 cm gives f = 340/(4×1.60) = 53.1 Hz, far too low.

Final answer: A