Particle's transverse oscillation path length

Steps:

• Frequency f = wave speed / wavelength = 48 cm/s / 12 cm = 4 Hz.
• Oscillations in 2 s: f × time = 4 Hz × 2 s = 8.
• Distance per oscillation: 4 × amplitude = 4 × 1.5 cm = 6 cm.
• Total distance: 8 × 6 cm = 48 cm.

Why C is correct:

• In transverse SHM, each particle travels 4A per cycle (equilibrium to +A and back, then to -A and back).

Why the others are wrong:

• A: Matches one wavelength, unrelated to particle's oscillatory path.
• B: Matches two wavelengths, irrelevant to vibration distance.
• D: Matches wave propagation distance (speed × time = 96 cm), not particle motion.

Final answer: C