When are the two vibrating particles said to be in same phase?

Correct option is D

The correct answer is (d) All of the above

Explanation:
• Particles are in the same phase when they are at the same displacement and moving in the same direction.
• Phase difference: Must be $2n\pi$ (where n = 0, 1, 2...), which is an even multiple of $\pi$.
• Path difference: Must be $n\lambda$, which is an even multiple of $\lambda/2$ (i.e., $2n \times \lambda/2$).
• Time interval: Must be $nT$, which is an even multiple of $T/2$.

Information Booster:
• If the phase difference is an odd multiple of $\pi$, the particles are in opposite phase.
• $\lambda$ is the wavelength and $T$ is the time period.

Additional Knowledge:
Option A
• Correct: 0, 2$\pi$, 4$\pi$ represents same state.
Option B
• Correct: $\lambda$, 2$\lambda$ corresponds to same phase.
Option C
• Correct: T, 2T represents the completion of full cycles.

So the correct answer is (d)