Antinodes in standing wave separated by λ/2

Steps:

• Positions of maximum loudness are antinodes in the standing sound wave.
• Moving from first to fourth antinode spans 3 intervals.
• Distance = 3 × (λ/2) = 0.12 m, so λ = (2 × 0.12 m) / 3 = 0.08 m.
• Frequency f = v / λ = 300 m/s / 0.08 m ≈ 4100 Hz.

Why A is correct:

• Matches f = 3v / (2 × distance) from standing wave antinode spacing of λ/2.

Why the others are wrong:

• B. Uses 4 intervals instead of 3, giving f ≈ 5000 Hz.
• C. Uses 6 intervals instead of 3, giving f ≈ 7500 Hz.
• D. Uses 8 intervals instead of 3, giving f ≈ 10000 Hz.

Final answer: A