Interference
Constructive vs destructive at φ = 0° / 180°.
Key Notes
Interference: superposition of two or more waves resulting in a new pattern of amplitudes.
CONSTRUCTIVE (in phase, Δφ = 2nπ): amplitudes ADD ⇒ A_total = A₁ + A₂.
DESTRUCTIVE (out of phase by π, Δφ = (2n+1)π): amplitudes SUBTRACT ⇒ A_total = |A₁ − A₂|.
Generally: A_total = √(A₁² + A₂² + 2A₁A₂·cos Δφ).
Intensity: I ∝ A² ⇒ I_max = (A₁ + A₂)², I_min = (A₁ − A₂)² for coherent sources.
COHERENT sources required: constant phase relation and same frequency.
Examples: Young's double slit (light), two loudspeakers (sound), two-source interference patterns.
Path difference Δx → phase difference Δφ = 2π·Δx/λ. Bright fringe: Δx = nλ. Dark fringe: Δx = (n+½)λ.
Formulas
Amplitude sum (two waves)
Vector sum of phasors.
Intensity ratio
Common form.
Max and min intensity (equal A)
When A₁ = A₂; constructive doubles A, intensity 4×.
Constructive condition
Path difference = integer wavelengths.
Destructive condition
Path difference = half-integer wavelengths.
Important Points
INTERFERENCE = wave addition. Constructive (in phase): amplitudes add. Destructive (antiphase): cancel.
Coherent sources REQUIRED — same f, constant phase relation. Otherwise pattern averages out.
Two equal-amplitude in-phase waves: intensity QUADRUPLES (not doubles) at constructive maximum.
Sunlight from two independent bulbs: NOT coherent, no observable interference pattern.
Laser light is highly coherent ⇒ clean interference patterns over long distances.
Active noise cancellation uses destructive interference of an inverted-phase signal.
Interference notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.