To demonstrate the phenomenon of interference, required two sources o…

The correct answer is Option (3) → same frequency and have a constant phase difference

A stable interference pattern needs coherent sources: sources of the same frequency whose phase difference stays constant in time, so that the bright and dark positions do not move.

Option (1) nearly the same frequency only — Incorrect. The same frequency alone is not enough; the phase difference must also stay constant.

Option (2) different wavelengths — Incorrect. Different wavelengths mean different frequencies, so the phase difference keeps changing and no steady fringes form.

Option (3) same frequency and have a constant phase difference — Correct. Same frequency with a constant phase difference makes the sources coherent.

Option (4) same frequency and have a rapidly changing phase difference — Incorrect. A rapidly changing phase difference shifts the fringes continually, and the pattern averages out to uniform illumination.

NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… Now if the two sources are coherent (i.e., if the two needles are going up and down regularly) then the phase difference φ at any point will not change with time and we will have a stable interference pattern; i.e., the positions of maxima and minima will not change with time. However, if the two needles do not maintain a constant phase difference, then the interference pattern will also change with time and, if the phase difference changes very rapidly with time, the positions of maxima and minima will also vary rapidly with time and we will see a “time-averaged” intensity distribution.”