Four independent waves are expressed as (i) y_1 = A_1 ω t (ii) y_2 = A_2 2ω t (iii) y_3 = A_3 ω t (iv) y_4 = A_4 (ω t + π/3) The interference between two of these waves is possible in (A) (i) and (iii) only (B) (iii) and (iv) only (C) (i), (iii) and (iv) only (D) All of them

PhysicsCBSE Class 12 · Board exam 2026, set 55/1/1 · 1 mark · MCQ

CBSE Class 12 Physics 2026: question 10

Set in the CBSE Class 12 board exam of 2026, paper 55/1/1, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q10 · 1 mark · MCQWave Optics

Four independent waves are expressed as
(i) $y_{1} = A_{1} sin ω t$ (ii) $y_{2} = A_{2} sin 2 ω t$
(iii) $y_{3} = A_{3} cos ω t$ (iv) $y_{4} = A_{4} sin (ω t + π /3)$
The interference between two of these waves is possible in

(A)(i) and (iii) only
(B)(iii) and (iv) only
(C)(i), (iii) and (iv) only
(D)All of them

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 55/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

What condition must two sources satisfy to interfere?

Hint 2

Compare the angular frequencies of the four waves.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Sustained interference needs coherent waves, i.e. the same frequency and a constant phase difference.
Waves (i), (iii) and (iv) all have frequency $ω$ with fixed phase differences, while (ii) has $2 ω$ . So the answer is (i), (iii) and (iv).
1 mark

Answer: (i), (iii) and (iv) only, option (C)

Where the marks are

Applies the coherence (same frequency) condition to choose (i), (iii), (iv) (1 mark)

Revise the chapter

Chapter: Wave Optics (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Wave Optics, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2026: question 10

Hints

Step-by-step solution

Revise the chapter

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