What are the parts of speech of "at" and "least" in "at least"?

In this instance, "least" is a noun meaning "smallest, lowest, or minimal amount."

Rephrasing the original sentence to demonstrate this meaning gives us: "Its lowest speed is faster than sound." Rephrasing Fumble Fingers's example sentence gives us: "A ton is its lowest possible weight," or, "The smallest weight it could have is a ton."

The rephrasing also helps clarify a more subtle point about the original sentence in question here. "At least" is taken as definitive, precise, and indicative of a specific point in a scale of measurement. So if the scale of measurement is speed, we might say "at least 700 miles per hour," or "at least the speed of sound." We would not usually say, "at least faster than the speed of sound," just as we would not usually say, "at least more than 700 miles per hour." "Faster" and "more than" are not defined points in the scale of measurement, and so they eradicate the functional bottom limit implied by "least." If something moves "at least faster than sound," its minimal speed can be any speed whatsoever as long as it is faster than the speed of sound.

One could argue that it is possible and reasonable to say "at least faster than sound," or in other words, "its slowest speed is nevertheless faster than the speed of sound." And I can't argue that this phrasing is impossible or non-reasonable. What I can argue, however, is that this phrasing is slightly awkward, and inconsistent with the well-accepted and useful intended meaning of "least." I would then say it is preferred for precision, effectiveness, and clarity of expression to use a single, specific point in a scale of measurement when you are referring to "the least."

I'd say at least is a quantifier - specifically, a proportional quantifier. That's what it's called in this paper, which also uses the term "cardinal quantifiers" when discussing at least n, at most n.

And as John Lawler comments (and he should know!) it could also be called a negative superlative quantifier. It's partly a matter of what terminological framework you're working in.

I suppose if we take a simpler case, such as "It weighs at least a ton", you could say the term functions as an "adjective" modifying ton, if that's the sort of terminology you want to use. I doubt it's worth trying to subdivide the component words into categories - you'd probably end up having to say least is an adjective, which might get messy.

Of course, you could say it adverbially modifies weighs in my example, and travels in OP's.

"At least" in the example given (faster than sound at least) is an adverb phrase qualifying faster. It is not a quantifier, as these qualify nouns, not adjectives, and at least does not qualify the word sound. Within the adverb phrase, at is a preposition and least is an adjective functioning as a noun.