Some enterprising researchers actually looked into this: in considerable detail and find that they did have the anatomical properties to enable speech:
“The Neanderthal voice box is a lot bigger than ours,” says Martelli. The voice box, or larynx, is essentially the echo chamber within which the voice resonates. A bigger, differently shaped echo chamber affects the phonetic quality of the sounds that come out of it. “We can get the model to produce a very convincing ‘oo’ and ‘ee’ sound, but the ‘ah’ comes out quite different.” The Neanderthal “ah,” it seems, would have been closer to “uh” or a combination of “ah” and “uh” that is difficult for us modern humans to render phonetically. (Readers in the United States should be able to watch a video here). Anna Goldfield, “The Neanderthal Throat—Did Neanderthals Speak?” at Sapiens
At the Sapiens site, Goldfield offers some sound files that might represent Neanderthal vs, current vocalization.
See also: Can we talk? Language as the business end of consciousness
Neanderthal Man: The long-lost relative turns up again, this time with documents
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