Superposition & Interference — Constructive, destructive
Waves & Sound
7
JEE Qs
8%
Hard
75
min
Master the precise conditions for constructive and destructive interference in terms of both path difference and phase difference, and their impact on resultant amplitude and intensity.
🧮 Key Formulas
✅ Key Points for JEE
- 1The principle of superposition states that the net displacement at any point and time due to two or more waves is the vector sum of the individual displacements due to each wave.
- 2Sustained interference patterns (fixed maxima and minima) require coherent sources, which means they must maintain a constant phase difference over time and have the same frequency.
- 3Constructive interference occurs when waves arrive in phase (Δφ = 2nπ or Δx = nλ), leading to maximum resultant amplitude (A_R = A1 + A2) and intensity.
- 4Destructive interference occurs when waves arrive 180° out of phase (Δφ = (2n+1)π or Δx = (2n+1)λ/2), leading to minimum resultant amplitude (A_R = |A1 - A2|) and intensity (which is zero if amplitudes are equal).
- 5Interference is a phenomenon of energy redistribution; energy is conserved overall, not created or destroyed. Regions of maximum intensity gain energy at the expense of regions of minimum intensity.
⚠️ Common Mistakes
- ✕Confusing path difference (Δx) with phase difference (Δφ) or using incorrect factors (e.g., λ/2π instead of 2π/λ for conversion).
- ✕Assuming destructive interference always leads to zero resultant intensity; this is only true for sources with equal amplitudes.
- ✕Forgetting that stable interference patterns are only observed with coherent sources (same frequency, constant phase difference).
📝 Practice Questions
See allQ27.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below ⎪ ⎪ 2025 (28 Jan Shift 1) JEE Main Previous Year Paper (1) Both A and R are true but R is NOT the correct (2) A is true but R is false explanation of A (3) A is false but R is true (4) Both A and R are true and R is the correct explanation of A
Q40.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170. Reason (R): Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below : (1) (A) is true but (R) is false (2) (A) is false but (R) is true (3) Both (A) and (R) are true and (R) is the correct (4) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A)
Q36.A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ρ1 and ρ2′ , respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1 : ρ2 = 1 : 16, then the length of the open tube is : (1) 15 7 cm (2) 207 cm (3) 15 9 cm (4) 209 cm
Q24.A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ( a−1a ) then the value of a is ________ → 2^i+6^j+8^k 2^i+^j+^k . The
Q24.Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is _______ Hz . (Velocity of sound in air = 333 m/s )
Q2. The equation of stationary wave is : y = 2a sin ( 2πntλ ) cos ( 2πxλ ). Which of the following is NOT correct : (1) The dimensions of n/λ is [T] (2) The dimensions of n is [LT−1] (3) The dimensions of x is [L] (4) The dimensions of nt is [L]
NCERT Chapters
- Class 11 Physics Ch 15: Waves