Particle's total vertical distance in SHM wave motion

Steps:

• Calculate period: T = 1/f = 1/15 s ≈ 0.0667 s.
• Find number of periods in 0.5 s: 0.5 / T = 7.5 periods.
• Total distance per full period: 4 × amplitude = 4 × 4 mm = 16 mm (from crest to trough and back).
• For 7 full periods: 7 × 16 mm = 112 mm; for half period from peak: 2 × 4 mm = 8 mm; total = 120 mm.

Why C is correct:

• In simple harmonic motion, particles travel 4A per full oscillation, and starting at peak, 7.5 periods yield exactly 30A = 120 mm by the SHM path length formula.

Why the others are wrong:

• A: Underestimates by using 0.5 s displacement (≈7.5A) instead of total path.
• B: Matches 2 full oscillations (15A), ignoring 7.5 periods.
• D: Erroneously uses speed × time with v = fλ = 1.8 m/s, yielding 900 mm horizontally.

Final answer: C