Question

Out of the given four waves (1), (2), (3) and (4)

y = a\sin(kx + \omega t) ......(1)

y = a\sin(\omega t - kx) ......(2)

y = a\cos(kx + \omega t) ......(3)

y = a\cos(\omega t - kx) ......(4)

emitted by four different sources $S_{1},S_{2},S_{3}$ and $S_{4}$ respectively, interference phenomena would be observed in space under appropriate conditions when

• A. Source $S_{1}$ emits wave (1) and $S_{2}$ emits wave (2)
• B. Source $S_{3}$ emits wave (3) and $S_{4}$ emits wave (4)
• C. Source $S_{2}$ emits wave (2) and $S_{4}$ emits wave (4)
• D. $S_{4}$ emits waves (4) and $S_{3}$ emits waves (3)

Answer 1

Answer: (C)

Source $S_{2}$ emits wave (2) and $S_{4}$ emits wave (4)

Answer 2

For interference, two waves must have a constant phase relationship. Equation ‘1’ and ‘3’ and ‘2’ and ‘4’ have a constant phase relationship of $\frac{\pi}{2}$ out of two choices. Only one S₂ emitting ‘2’ and S₄ emitting ‘4’ is given so only (3) option is correct.