The displacements of four light waves are given below. If the amplitudes $a_1$ and $a_2$ are nearly equal, then the interference fringes may be observed due to superposition of
(A) $y = a_1\sin wt$
(B) $y=a_2\sin (wt + \phi)$
(C) $y = a_1\sin 2wt$
(D) $y = a_2\sin 3(wt + \phi)$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (B) only
Interference fringes are observed when two waves have:
1. Nearly equal amplitudes
2. The same frequency
Given waves:
(A) $y = a_1 \sin \omega t$
(B) $y = a_2 \sin (\omega t + \phi)$
(C) $y = a_1 \sin 2\omega t$
(D) $y = a_2 \sin 3(\omega t + \phi)$
Waves (A) and (B) have the same frequency $\omega$ and nearly equal amplitudes → can produce interference fringes.
Answer: (A) and (B)