Question

Two particles A and B have a phase difference of π when a sine wave passes through the region.
(a) A oscillates at half the frequency of B.
(b) A and B move in opposite directions.
(c) A and B must be separated by half of the wavelength.
(d) The displacements at A and B have equal magnitudes.

Answer 1

(b) A and B move in opposite directions.
(d) The displacements at A and B have equal magnitudes.


A and B have a phase difference of π. So, when a sine wave passes through the region, they move in opposite directions and have equal displacement. They may be separated by any odd multiple of their wavelength.
$\overrightarrow{y_A}=A\sin \left(\omega t\right)$
$\overrightarrow{y_B}=B\sin \left(\omega t+\mathrm{\pi }\right)$