Wave oscillation at half period inverts displacement

Steps:

• Frequency f = 0.5 Hz, so period T = 1/f = 2 s.
• Time t = 1 s is T/2, half a period.
• Point P on the rope undergoes simple harmonic motion with the wave.
• At t = T/2, displacement y(T/2) = -y(0), inverting the original position.

Why B is correct:

• B shows the inverted displacement, matching y(t) = A sin(ωt + φ) where sin(φ + π) = -sin(φ) at half period.

Why the others are wrong:

• A is the original position, unchanged after half period.
• C likely shows a quarter-period shift, not half.
• D probably indicates full period or unrelated phase.

Final answer: B