Under what parameters? There are about 6000 languages out there with many dialects in each-- in fact, I'd say that there might be nearly 7 billion different acoustic signatures out there

Determining the language would depend on:
1. Whether you are looking for specific clues or attempting to categorize
any sample at all regardless of what information it contains.
2. Some way of standardizing the samples. Across all languages, males and females would be very different acoustically, probably MORE than the linguistic variation. You'd get lots of acoustic fingerprints, but you'd need some standardization to use that for anything.
3. The size of your comparison set. If you're just choosing between, say, 5 languages, that would be attainable probably. If you're choosing from 6000 + various dialects, that's almost unimaginable.
4. It would depend on the quality of your training data.
As a hypothetical answer, consider that machines are not as good at language as we are. Therefore, assume that they are. How quickly can a human recognize a language? Especially when that human knows several related languages, it might take a sentence or two to really know. So, I don't know... best case scenario at least 10 seconds for real reliability? Maybe more. And that's assuming a perfected machine that works at the level of a human. Certainly a machine MIGHT have an advantage for certain acoustic details, but at least at this point I don't think the technology is there; what the machine hears that we don't isn't actually helpful in this kind of process.