Fixed point oscillation in a traveling wave

Steps:

• Identify the wave profile at t=0: displacement varies sinusoidally with distance, indicating a transverse wave.
• Point P is fixed in space, so its motion follows the wave's temporal variation at that position.
• For a traveling wave, displacement at P is s = A sin(ωt + φ), where φ depends on P's position in the profile.
• Match the graph showing sinusoidal oscillation starting from P's initial displacement.

Why D is correct:

• D shows sinusoidal variation with correct phase matching P's position at t=0, per the wave equation s(x,t) = A sin(kx - ωt).

Why the others are wrong:

• A: Incorrect phase; starts at maximum displacement, not P's initial value.
• B: Wrong frequency; period doesn't match wave speed from profile.
• C: Non-sinusoidal shape; waves on water are approximately sinusoidal.

Final answer: D