Round 1/6Score 0
Wave Packet Lab
Build Fourier waveforms and separate group from phase velocity.
Challenge
Live model
A wave packet is a carrier oscillation within a travelling envelope.
The physics
Six-term Fourier sine series: y(t) = Σ Aₙ sin(2πnft + φₙ). RMS = √mean[(target − player)²]. Dispersion: ω = ck + βk², vₚ = ω/k, v_g = dω/dk = c + 2βk. Here c = 2 m/s and β = 0.5 m²/s. Gaussian packet shown with a narrow-band approximation.