Instructions:

The Dispersive Wavepacket Plotter displays a superposition of travelling waves:

y=Σ_k a_k cos(kx-ω(k)t). The wavevectors k are consecutive integers. You can set the maximum and minimum values of k using the increment and decrement buttons in the Control Panel, or by text entry in the box. Having made your choice, click Make Wavepacket and the wave is displayed at t=0

To display the time development, either click Increment T to step forward in time, or the Video button to Start or Stop continuous motion.

The angular frequencies ω(t) are given by a dispersion relation. There is a choice of three:

Surface waves on Water: ω²=gk where g is the acceleration due to gravity, 9.81 m s^-2.
Unit of length is 1 m and Unit of time 1 s.
This is appropriate for water waves with k<80 m^-1.

Capillary waves on Water: ω²=(σ/ρ)k³ where σ is the surface tension and ρ the density of water σ/ρ =7.4 10^-5 m³s^-2.
Unit of length is 0.01 m and Unit of time 0.01 s.
This is appropriate for water waves with k>800 m^-1
(i.e. enter k>8).

Surface/Capillary waves: ω²=gk+(σ/ρ)k³.
Unit of length is 0.1 m and Unit of time 0.1 s.
This is in principle correct for all k, but is essentially equivalent to the simpler cases for k>800 m^-1 or k<80 m^-1
(i.e enter k between 8 and 80).

Interesting cases occur around:
k=145 m^-1 (enter 14): the minimum of v_g: nearly perfect envelope approximation;
k=364 m^-1 (enter 36): the minimum of v_p: v_g=v_p, so apparently non-dispersive.