Wave Packet Composer & Dispersive Superposition Simulator

Wave Superposition $\psi(x,t)$

Envelope $|A(x,t)|$

Carrier Crests ($v_p = \omega_0/k_0$)

Group Envelope Peak ($v_g = d\omega/dk$)

Phase Velocity ($v_p$)

240.0 m/s

Carrier wave speed $\omega_0/k_0$

Group Velocity ($v_g$)

200.0 m/s

Envelope energy speed $d\omega/dk$

Dispersion Regime

Normal ($v_p > v_g$)

Crests overtake packet

Envelope Broadening

42.0 nm

Temporal chirp spreading

Interactive Probe at Pointer $x = 0.0 \mu m$

Instantaneous Amplitude $\psi(x,t)$:0.00

Envelope Magnitude $|A(x,t)|$:0.00

Local Instantaneous Phase:0.00 rad

Physical Presets

Wave Mechanics & Medium

Carrier Frequency ($\omega_0$) 440 Hz

Dispersion Curvature ($d^2\omega/dk^2$) +0.40

Envelope Spatial Width ($\sigma_0$) 42 px

Wave Base Velocity ($v_0$) 240 m/s

Fourier Harmonics ($k_1 \dots k_6$) Click/Drag Bars

Separate wave-packet equations from preset names

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Read the explanation

The source export samples a Gaussian envelope centered at pixel two hundred. At offset zero, its envelope is one; at offset one chosen width, it is exponential minus one half, about zero point six zero six five. At two widths it is exponential minus two, about zero point one three five three. The harmonic sum is multiplied by this envelope. The bars use those actual ratios. The Gaussian preset uses base velocity two hundred forty and dispersion curvature zero point four. Its displayed group velocity is base velocity times one minus zero point four times curvature, giving two hundred one point six. The anomalous preset uses base two hundred twenty and curvature minus zero point six, giving two hundred seventy two point eight. This is the site’s chosen teaching rule, not an independently derived physical dispersion relation. The preset called soliton sets dispersion curvature to zero, so displayed phase and group velocities both equal two hundred sixty. Its exported envelope is still Gaussian and its waveform is still a finite cosine harmonic sum. The source does not solve a nonlinear soliton equation in this exported snapshot. Forty one samples, from zero to four hundred pixels in increments of ten, preserve the full plotted configuration and spatial evidence.