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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.
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Solution
(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.
\[\vec{y_A} = A\sin\left( \omega t \right)\]
\[\vec{y_B} = B\sin\left( \omega t + \pi \right)\]
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