Wave 1 (Blue)
Wave 2 (Red)
Superposition (y₁ + y₂)
Beat Pattern
Amplitude at x=0
Phase Difference
Wave Energy
Wave Parameters
Wave 1 (Blue)
Wave 2 (Red)
Display Settings
Quick Presets
Wave Equations
What is Wave Superposition?
Wave superposition is the fundamental principle that when two or more waves overlap in space, the resultant displacement is the algebraic sum of the individual displacements at each point. This principle applies to all types of waves including sound, light, water waves, and matter waves.
Constructive and Destructive Interference
When two waves with the same frequency overlap, they can interfere constructively (in phase, amplitudes add) or destructively (out of phase, amplitudes subtract). Maximum constructive interference occurs when the phase difference is 0, 2π, 4π..., while maximum destructive interference occurs at π, 3π, 5π...
Beat Phenomenon
When two waves with slightly different frequencies (f₁ ≈ f₂) interfere, they create a beat pattern. The resulting wave oscillates at the average frequency but has an amplitude that varies at the beat frequency f_beat = |f₁ - f₂|. This is commonly observed in music when tuning instruments and creates the characteristic "wah-wah-wah" pulsating sound.
Applications
Wave superposition has countless applications: noise-canceling headphones use destructive interference to eliminate unwanted sounds, radio tuners use superposition to select frequencies, musical harmony relies on superposition of sound waves, optical interferometry enables precise measurements at nanometer scales, and quantum mechanics is fundamentally based on wave superposition principles.