Standing wave nodes separated by λ/2

Steps:

• Intensity minima occur at nodes in the standing wave formed by the incident and reflected sound.
• Distance between consecutive nodes is λ/2.
• From X (initial minimum) to Y (final minimum), the microphone passes through 4 additional minima, for 6 minima total and 5 intervals.
• Total distance XY = 5 × (λ/2) = 70.0 cm, so 5λ/2 = 70.0 cm.

Why D is correct:

• Solving 5λ/2 = 70.0 gives λ = (2 × 70.0)/5 = 28.0 cm, matching the node spacing in standing waves.

Why the others are wrong:

• A: 17.5 cm implies 8 intervals (70.0 / (17.5/2) = 8), but only 5 intervals fit the minima count.
• B: 14.0 cm implies 10 intervals (70.0 / (14.0/2) = 10), exceeding the described minima.
• C: 23.0 cm implies ~6.1 intervals (70.0 / (23.0/2) ≈ 6.1), not an integer matching 5.

Final answer: D