Breakdown of Wartest du auf den Studenten?
du
you (informal singular)
warten auf
to wait for
der
who, which, that (relative pronoun; die, das)
der Student
the university student
Questions & Answers about Wartest du auf den Studenten?
Why is there an "-en" at the end of Studenten? Is it plural?
No, it is actually singular here ("the student"). Student is part of a special group of masculine nouns called "weak nouns" (or N-declension nouns). These nouns add an -n or -en in every case except the nominative (when they are the subject of the sentence).
If Studenten is singular here, how would I say "Are you waiting for the students?" (plural)
You would say Wartest du auf die Studenten? The noun itself looks exactly the same, so you have to look at the article to tell if it's singular or plural. The accusative plural article is die, while the accusative masculine singular article used here is den.
Why does the sentence use auf? Doesn't auf usually mean "on"?
It often does, but prepositions rarely translate word-for-word between English and German. In German, the verb warten (to wait) is paired with the preposition auf to express "waiting for" someone or something. It is best to memorize the phrase warten auf as a single block.
Why is den in the accusative case here instead of the dative case?
The phrase warten auf always requires the accusative case for the person or thing you are waiting for. Because Student is a masculine noun, the accusative article becomes den.