Practice question

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. At a fixed end, the displacement must be zero, requiring the reflected wave to be out of phase by π radians (inverted) to cancel the incident wave at the boundary. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields It reflects with a phase change of π radians, illustrating frequency-length-speed interdependence and quantization by boundaries.