I would like to plot (or to find) an animation where two waves at different frequencies, propagating with different velocities, sum together
$$w_1 (x,t) = \cos(\omega_1 t - k_1 x)\\w_2 (x,t) = \cos(\omega_2 t - k_2 x)$$
and generate the resulting signal
$$w(x,t) = \cos(\omega_1 t - k_1 x) + \cos(\omega_2 t - k_2 x)$$
An envelope and a carrier can be distinguished after some algebra and the animation should show the different propagation velocities of the envelope and the carrier.
1) Is there a site which already provides this? This page (last image) and this page provide different animations and are not suitabile. In fact, the first link (last image of the webpage) doesn't show $w_1$ and $w_2$ moving at different velocities, but just at the same velocity. The second link does never show the three waveforms $w_1$, $w_2$ and $w$ separately
2) Is there a free tool / software / site to generate such an animation?