Particle Displacement in Transverse Waves Follows Sinusoidal Motion

Steps:

• Examine the diagram at t=0 to find particle X's initial displacement and direction of motion.
• Note the wave travels left to right, so X's displacement oscillates with period T as the wave profile passes.
• For a standard transverse wave, displacement y = A sin(ωt + φ), where phase φ depends on X's position at t=0.
• Over 2T, the graph completes two full cycles, starting from X's initial state.

Why B is correct:

• B matches the upward-starting sine wave, as particle X at t=0 is at equilibrium and begins moving upward, per the wave's crest approaching from the left (sine wave definition y = A sin(2πt/T)).

Why the others are wrong:

• A shows a downward-starting sine wave, contradicting X's initial upward motion.
• C depicts a cosine-like downward oscillation, mismatched to the phase at t=0.
• D is an inverted upward sine, opposite to the wave's transverse direction.

Final answer: B