The fabled pastor of my home parish, the late Msgr. Richard Schuler told stories about being in Rome when Ven. Pius XII infallibly declared the Assumption of the Blessed Virgin to be a dogma of the Faith. He was present for the procession with the icon of Salus Populi Romani and for the proclamation.
Here is a video about the event in 1950.
And there is this… just after 26:00 you hear Pius reading the actual Proclamation of the Dogma.
Ah, so this is what it looks like when the Pope speaks ex cathedra and declares something infallible.
The Church should use this as an example of such in a PSA so that everyone will know how to tell the difference between speaking infallible and declaring a dogma from saying whatever comes to mind at the moment that may or may not be ambiguous or confusing.
When I was growing up, this is how video of an important event was delivered — at the movies! Pathe News. No live streaming. No internet. No twitter. Nothing but news of the world in between two movies, cartoons, coming attractions and being chased out of the adult section by the flashlight carrying matron.