Two sources are producing waves as given in the options below. Which two sources are called coherent?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → having a constant phase difference
Two sources are coherent when the phase difference between the waves they emit does not change with time. Only then do the waves coming from them give a steady interference pattern, with fixed positions of maxima and minima.
Why the other options are incorrect
Option (1) of same velocity — Incorrect. Waves of the same kind in the same medium always have the same velocity, whether or not their sources are coherent.
Option (2) of equal wavelength — Incorrect. Equal wavelength (equal frequency) is needed but is not enough by itself: two separate lamps of the same colour still have no fixed phase relation. The defining condition is the constant phase difference, which also implies equal frequency.
Option (4) having wavefront of same shape — Incorrect. The shape of the wavefront says nothing about the phase relation between the two sources.
NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… Consider two needles S1 and S2 moving periodically up and down in an identical fashion in a trough of water [Fig. 10.8(a)]. They produce two water waves, and at a particular point, the phase difference between the displacements produced by each of the waves does not change with time; when this happens the two sources are said to be coherent.”