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#destructive interference

2 public questions tagged with this topic.

Which wave phenomenon is responsible for the cancellation of sound in certain regions when two speakers emit waves of eq

**Interference of waves** produces enhancement or cancellation based on phase. Two equal amplitude waves out of phase by π cancel completely, A = 0, while in-phase superposition doubles amplitude to 2a, demonstrating energy redistribution without violation of conservation. Destructive interference occurs when two waves of equal frequency are out of phase (e.g., by π radians), resulting in zero net displacement in specific regions. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Destructive interference, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

What happens to the amplitude of two identical waves undergoing destructive interference when their phase difference is

**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. For two identical waves with phase difference Φ = π , the resultant amplitude is A = 2a cos(Φ/2) = 2a cos(π/2) = 0 , leading to complete cancellation. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Becomes zero, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves