This is the sting. It opens this piece by Dvorak. Where does it come from and what is it called? Why is it such a common fanfare sting? Why is it associated with "ta-da"? To leave no stone unturned, what are those two chords?
It's called the "ta-da" sting because it has exactly the same rhythm, melody and inflection as the phrase "Ta-da!" which is used commonly when a person produces something, as if by magic. That's the easy part of the question.
The harder question is "why." The standard explanation is that the phrase is a vocal imitation of a fanfare, such as the one at the start of Dvorak's piece, and the syllables are just non-lexical nonsense syllables such as those used in scatting.
HOWEVER, I did find this plausible etymology on "Urban Dictionary":
Ta-dah! comes from the Bulgarian or Slavic words for "ta + da" (та да!)meaning "that there". It is an exclamation used in magic shows (prestidigitation) by magicians to announce the conclusion of the trick or the illusion to the audience.
The equivalent to 'Voila!' in French. It was likely a Bulgarian or Russian magician (definitely Eastern European) traveling in the United States that said it (likely in the late 1800's when Eastern European immigrants started flooding to American shores).
An American likely heard it and thought it sounded usuable for showmanship, without knowing what it was. та да! Then magicians everywhere started using it as a handle or a gimic because it sounded more impressive than saying "There you have it!" in English.
The Bible in Bulgarian, shows this sort of usage: "Behold!" "Voila!" and "та да!" Mean roughly the same thing. It is often used as an introductory to a sentence, mainly where God is speaking, but by itself is showmanship flourish.
(Urban Dictionary is not typically considered a reputable source, but a little bit of independent Googling confirms this is an actual Bulgarian phrase, found frequently in the Bible, and with the same general meaning outlined.)
Dvorak, we recall, is himself Slavic, as is the piece of music in question. So perhaps the musical phrase was actually copied from the spoken one, not the other way around. In which case, the reason they are such close reflections of each other is because they have a common origin.