Fundamental frequencies in organ pipes

Steps:

• Stationary waves in pipes require nodes/antinodes at ends: closed end is node, open end is antinode.
• For closed pipe (one end closed), fundamental mode has length L = λ/4, so frequency f_closed = v/(4L).
• For open pipe (both ends open), fundamental mode has L = λ/2, so f_open = v/(2L).
• Thus, f_closed = (1/2) f_open, so closed pipe has lowest fundamental frequency for same length.

Why B is correct:

• B is closed at one end; its fundamental frequency is half that of an open pipe of equal length, per the quarter-wavelength resonance condition.

Why the others are wrong:

• A (open both ends): Higher fundamental frequency due to half-wavelength mode.
• C (likely longer pipe or different config): Cannot produce lower frequency than closed pipe's fundamental.
• D (likely open or mismatched): Frequencies start higher than closed pipe's lowest mode.

Final answer: B