Wave Interference Physics Simulation

AMPLITUDE (A)

Definition: The maximum displacement of a wave from its equilibrium position (rest position).

Key Points:

• Measures the strength/intensity of the wave
• Always a positive value
• Determines how loud (sound) or bright (light) the wave is
• Unit depends on wave type (meters for displacement, volts for electrical)

Examples:

• Sound: Higher amplitude = Louder sound
• Light: Higher amplitude = Brighter light
• Ocean: Higher amplitude = Bigger waves

PHASE (φ)

Definition: The position of a wave at a specific point in its cycle, measured in degrees (0°-360°) or radians (0-2π).

Key Points:

• Determines where the wave starts in its cycle
• Controls the horizontal shift of the wave
• Two waves with same frequency but different phase will be offset
• Phase difference determines interference type

Phase Relationships:

• 0° (In Phase): Waves peak together → Constructive interference
• 90° (Quadrature): One wave peaks when other crosses zero
• 180° (Out of Phase): Waves opposite → Destructive interference

Wave Equation

y = A sin(2πft + φ)

Where:

• y = Displacement at time t
• A = Amplitude (maximum displacement)
• f = Frequency (cycles per second)
• t = Time
• φ = Phase (starting position)

Phase in Practice:

• φ = 0°: Wave starts at zero, going up
• φ = 90°: Wave starts at maximum
• φ = 180°: Wave starts at zero, going down
• φ = 270°: Wave starts at minimum

Practical Examples

Amplitude Examples:

• Guitar String: Pluck harder = Higher amplitude = Louder sound
• Earthquake: Richter scale measures amplitude of seismic waves
• Radio: AM radio varies amplitude to encode information

Phase Examples:

• Stereo Speakers: Wrong phase = Sound cancellation
• AC Power: 3-phase power has phases 120° apart
• MRI Scanning: Uses phase differences for imaging

Superposition Principle

When two or more waves meet at the same point, their amplitudes add algebraically (superposition principle).

y_total = y₁ + y₂

The resulting wave's amplitude depends on the phase relationship between the waves.

Types of Interference

Constructive Interference:

• Phase difference = 0°, 360°, 720°... (even multiples of 180°)
• Waves reinforce each other
• Resultant amplitude = |A₁ + A₂|
• Maximum energy transfer

Destructive Interference:

• Phase difference = 180°, 540°... (odd multiples of 180°)
• Waves cancel each other
• Resultant amplitude = |A₁ - A₂|
• Energy redistribution, not destruction

Real-World Applications

Constructive Interference:

• Laser Technology: Coherent light waves amplify
• Concert Halls: Sound waves focused to audience
• Radio Telescopes: Multiple antennas combine signals
• Medical Ultrasound: Focused beams for imaging

Destructive Interference:

• Noise-Cancelling Headphones: Cancel ambient noise
• Anti-Reflective Coatings: Reduce glare on glasses
• Sound Studios: Acoustic dampening
• Stealth Technology: Cancel radar reflections

Mathematical Analysis

For two waves with equal frequency:

Wave 1: y₁ = A₁ sin(ωt + φ₁)

Wave 2: y₂ = A₂ sin(ωt + φ₂)

Resultant: y = y₁ + y₂

Phase Difference: Δφ = φ₂ - φ₁

• If Δφ = 0°: Perfect constructive, A_result = A₁ + A₂
• If Δφ = 180°: Perfect destructive, A_result = |A₁ - A₂|
• Other angles: Partial interference