Hello.
I am watching this video:
https://www.youtube.com/watch?v=xIQtnQ9XPbE

and he says there:

I see that the wave turns into a "normal" sinus in the end, but it's not constant.
I think, that even on an unmatched transmission line, the waves should go back and forth, but eventually turn into a constant voltage. Isn't that correct?
If not, and the correct answer is that the steady state IS the final wave there - how do I calculate the voltage? is it the RMS of the wave?

When a TEM wave in a cable goes from one medium (cable) to another, If there is an impedance mismatch (and the signal source is a voltage source), there is a reflection and a standing wave. Furthermore if the propagation velocity changes, the waves "pile up" in the downstream cable. There are two equations that are relevant:

Cable impedance is proportional to

Z = sqrt(1/ε)

and the propagation velocity is proportional to

and v = βc = 1/sqrt(ε)

where ε is the dielectric constant of the dielectric in the cable. A high dielectric constant reduces both the cable impedance and the propagation velocity.

If the signal source impedance does not equal the cable impedance, there is a reflection of the backward-propagating signal, producing a standing wave.