Final answer:
Two particles with a phase difference of π result in displacements with equal magnitudes but opposite directions, indicating that they are half a wavelength apart. The frequency of oscillation will be the same for both particles. The correct answer is option A., B. and C.
Step-by-step explanation:
When two particles have a phase difference of π, it indicates that they are out of phase; specifically, they are half a cycle out of phase with each other. Consequently, when a sine wave passes through such particles:
- The displacements at points A and B have equal magnitudes but in opposite directions, thereby validating the assertion that A and B move in opposite directions (due to opposing phases).
- It is also true that points A and B must be separated by half of the wavelength, which is characteristic of points with a phase difference of π in a sine wave.
The statement that A oscillates at half the frequency of B is incorrect since the frequency of oscillation is a property of the wave itself and does not vary between different points along the wave.