Sine Wave Phase Calculator

Understanding Sine Wave Phase

Sine Wave Components

y(t) = A sin(2πft + φ)

where:

  • A = Amplitude
  • f = Frequency
  • t = Time
  • φ = Phase shift (in radians)
  • 2πf = Angular frequency (ω)

Phase Relationships

Phase Angle

  • Instantaneous phase = ωt + φ
  • Phase difference = Δφ
  • Period relationship: 2π = 360°

Phase Velocity

  • v = ω/k
  • k = wave number
  • λ = wavelength = v/f

Wave Properties

Energy

  • Average power = A²/2
  • RMS value = A/√2
  • Peak-to-peak = 2A

Superposition

  • Constructive interference
  • Destructive interference
  • Standing waves

Phase Modulation

  • PM modulation index
  • Sidebands generation
  • Bessel functions

Applications

Signal Processing

  • Phase detection
  • Lock-in amplifiers
  • Phase-locked loops

Communications

  • Phase modulation
  • QPSK encoding
  • Phase coherence

Quantum Mechanics

  • Wave functions
  • Phase coherence
  • Berry phase