Phase difference in progressive wave graphs indicates feature separation

Steps:

• Examine the displacement-time graphs for phase relationship between particles.
• Identify 180° phase difference, meaning displacements are opposites (one inverted sine wave).
• Calculate separation: phase shift π radians gives distance d = λ/2 = 10 cm (particles' spacing).
• Match to wave type: in longitudinal waves, λ/2 separates compression (bunched particles, positive displacement) from nearest rarefaction (spread particles, negative displacement).

Why A is correct:

• Longitudinal waves have compressions and rarefactions alternating every λ/2; 10 cm spacing positions particles at these features, matching opposite-phase oscillations.

Why the others are wrong:

• B: 20 cm separation implies λ/2 = 20 cm, but particles are 10 cm apart.
• C: Transverse peak-trough is λ/2 = 20 cm, exceeding 10 cm particle spacing.
• D: Adjacent peaks are λ = 10 cm apart, yielding 0° phase difference and identical graphs.

Final answer: A