A and B are two interfering sources where A is ahead in phase by 54° relative to B. The observation is taken from point P such that PB - PA = 2.5 λ. Then the phase difference between the waves from A and B reaching point P is (in rad) (a) 3.5π (b) 5.3π (c) 4.3π (d) 5.8π

Answer: (b). Wave from B travels 2.5λ more, so it lags by (2π)/(λ)(2.5λ) = 5π. A is already ahead by 54° = 54/180π = 0.3π. Both effects put A ahead: total = 5π + 0.3π = 5.3π. So the answer is (b) 5.3π.

A and B are two interfering sources where A is ahead in phase by 54°… | MHT CET 2023 (13 May, Shift 1)

Q59MHT CET 2023 · 13 MAY · SHIFT 1Medium

Superposition, Coherence & Intensity

$A$ and $B$ are two interfering sources where $A$ is ahead in phase by $54^\circ$ relative to B. The observation is taken from point $P$ such that PB $-$ PA = 2.5 $\lambda$ . Then the phase difference between the waves from A and B reaching point P is (in rad)

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Answer: (b)

Wave from $B$ travels $2.5\lambda$ more, so it lags by $\dfrac{2\pi}{\lambda}(2.5\lambda) = 5\pi$ .
$A$ is already ahead by $54^\circ = \dfrac{54}{180}\pi = 0.3\pi$ .
Both effects put $A$ ahead: total $= 5\pi + 0.3\pi = 5.3\pi$ .
So the answer is (b) $5.3\pi$ .

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