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. Compare with y = a sin (kx - ω t) , ω = 80 rad/s . Frequency: v = (ω/2π) = (80/2π) ≈ 12.73 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 13 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.