What gives rise to racial accents? (timbre)

There are several elements to this issue:

1. Your ability to identify ethnicity is much more likely to be a result of perceiving cultural styles of speaking than anything physiological. You would most likely not be able to replicate this with speakers of other English accents. And even less likely if the speaker was just uttering individual sounds without intonation.

2. You are probably much worse at this than you think. This sort of thing is incredibly prone to bias. Particularly when it comes to race, you should immediately assume that any generalizations you formulate based on your experience are biased as are your perceptions of any particular instances upon which the generalizations are based.

3. Just like it is difficult to draw a boundary between languages and dialects, it is even more difficult to draw boundaries between 'races'. Nevertheless, some studies seem to show differences in formant frequencies across languages - this paper gives a good summary of some of the research. There were also some some significant trends in the configuration of vocal tract (however, with huge in-group variation).

But these findings do not necessarily imply anything straightforwardly deterministic about race and the voice (even if we were to accept an unproblematic definition of race). The key quote from the paper is this (my emphasis):

To the anthropologists and linguists, the findings also implied that not all formant frequencies of even a neutral utterance carefully designed to have maximally reduced specific language/dialect influences, could be completely accounted for solely by vocal tract parameters. As was indicated in the previous paragraph, there may not be a linear correlation between length and volumetric parameters with the acoustic outputs. In other words, factors other than morphological differences, such as dialect (Yang, 1996), the effect of air perturbation (Mayo & Grant, 1995), a wide range of speech style, and other cultural-linguistic characteristics may all bring about significant changes to the vocal output of the speakers.