Progressive Wave Equation (y(x,t) = a sin(kx - ωt + φ))
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y(x,t) = a sin(kx - ωt + φ)
What each symbol means
| Symbol | What it stands for |
|---|---|
| a | Amplitude of wave (m) |
| k | Angular wave number = 2π/λ (rad/m) |
| φ | Initial phase (rad) |
| ω | Angular frequency = 2π/T = 2πν (rad/s) |
| y(x,t) | Displacement of medium element at position x and time t |
| (kx - ωt + φ) | Phase of wave |
When to use this
Describes sinusoidal wave travelling in +x direction. For wave in -x direction: y = a sin(kx + ωt + φ). Each particle executes SHM with same ω and a but different phase. The function must have x and t in combination (kx ± ωt) to represent a travelling wave. NCERT Eq. 14.2.