Characersitics of a traveling wave on a half wave dipole antenna
There are only standing waves of voltage and current on a resonant dipole antenna, not travelling waves.
It is the current that reverses direction, after traversing the length of the antenna, every half cycle.
This phenomenon is well demonstrated in the Wikipedia animation.
Travelling waves of voltage and current exist only on a non-resonant dipole antenna.
Here's an animation of a travelling wave.
https://upload.wikimedia.org/wikipedia/commons/9/91/1D-Wave.gif
A standing wave of voltage or current shows the unchanging value of either along the length of the antenna.
A travelling wave, on the other hand, shows the constantly changing values along  its length.