Q. Out of the given 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) Sources $S_{1}$ 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)
Explanation
(c) 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 $S_{2}$ emitting ‘2’ and $S_{4}$ emitting ‘4’ is given so only (c) option is correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.