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 rigid boundary, phase changes by π . Incident: y_i = 0.05 sin (10x - 20t) . Reflected: y_r = -0.05 sin (10x + 20t) . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields y = -0.05 sin (10x + 20t), illustrating frequency-length-speed interdependence and quantization by boundaries.