Two particles A and B have a phase difference of n 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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(b) A and B move in opposite directions.
(d) The displacements at A and B have equal magnitudes.
EXPLANATION:
The frequencies of the particles will be the same, so the option (a) is not true.
Let the displacement of the particle at A be y = A' sin(⍵t-kx) and of the particle at B be y' = A' sin(⍵t-kx+π) = -A' sin(⍵t-kx)
So, y = -y'.
Thus A and B move in opposite directions and the displacements at A and B have equal magnitudes.
So, the options (b) and (d) are true.
When the phase difference of A and B is π, the separation between them maybe (nλ+λ/2) = (2n+1)λ/2, where n = 1, 2, 3,....... The option (c) is a special case, hence not true.
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