Two coherent sources $$\(X\)$$ and $$\(Y\)$$ of microwaves of frequency $$\(2.5 \times 10^{10} \mathrm{~Hz}\)$$ are a distance of 0.18 m apart in a vacuum, as shown in Fig. 6.1. Fig. 6.1 (not to scale) There is a phase difference of $$\(90^{\circ}\)$$ between the waves emitted at the two sources. A microwave detector moves along the line PQ , which is parallel to the line joining the two sources and 2.3 m away from it. Point $$\(O\)$$ is on the line $$\(P Q\)$$ at a position that is equidistant from the two sources. Point $$\(A\)$$ is the position on line $$\(P Q\)$$ where the intensity of the microwaves is the greatest. Explain why the position of greatest intensity is not at point O . ....................................................................................................................................... . ....................................................................................................................................... . ....................................................................................................................................... . ................................................................................................................................. (ii) On Fig. 6.1, draw a cross $$\((x)\)$$ to show the position of the point on line $$\(P Q\)$$ where the intensity minimum that is the closest to point $$\(O\)$$ occurs. Label this point $$\(B\)$$.

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