Case: Read the passage and answer the question.
A wave is represented by a variable y which gives the displacement of the particles of the medium in which the wave is travelling at any given instant of time. In the same context, consider two waves y1 and y2 which superpose such that y gives the resultant of the two waves.
What is y equal to?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → The vector sum of \( y_1 \) and \( y_2 \)
Option (1) The vector sum of \( y_1 \) and \( y_2 \) — Correct. The superposition principle says that the resultant displacement at a point is the vector sum of the displacements of the separate waves, \( y=y_1+y_2 \). The direction of each displacement is taken into account.
Option (2) The scalar sum of \( y_1 \) and \( y_2 \) — Incorrect. A scalar sum adds the sizes of the displacements without their directions. Two equal displacements in opposite directions would then give twice the displacement. But their true resultant is zero. So a scalar sum cannot explain destructive interference.
Option (3) The dot product of \( y_1 \) and \( y_2 \) — Incorrect. A dot product multiplies the two displacements. It gives a quantity in square metres, which is not a displacement. So it cannot be the resultant displacement of the medium.
Option (4) The vector product of \( y_1 \) and \( y_2 \) — Incorrect. A vector product also has the unit of area. It is zero for two displacements along the same line. So it does not give the combined displacement either.
NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… Indeed the entire field of interference is based on the superposition principle according to which at a particular point in the medium, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each of the waves.”