Primate phonetics

Primates vocalize, but different primates vocalize in different ways. Some prosimians formerly thought to be mute actually do ultrasonic vocalizations and have ultrasonic hearing.

The pointless surplus of human phonemes
Differences in the larynx place the tongues and vocal cords of nonhuman primates in a position unsuited for emulating human speech. Nonhuman primates have a more limited phonetic potential. Geladas use slightly more than 30 phonemes, and cottonhead tamarins use 40. Great Apes with their partly humanized vocal tracts can therefore be expected to have the anatomy for pronouncing 60-70 phonemes, which is far less than the hundreds that humans can pronounce. However, it is enough for not being the limiting factor on their ability to invent their own languages. After all, most Indo-European languages only use about 30 phonemes give or take a few (although some slavic languages use over 40), in other language families some Khoisan languages with their inclusion of clicks are known to use over 100 phonemes, but Hawaiian use only 13 (other Polynesian languages also use 20 or less), and the Papua New Guinean language Rotokas use only 11. Yet none of these languages are limited in what information can be expressed, it would be possible to translate Hamlet or the theory of relativity even to Rotokas. The Piraha language in the Amazon with only 10 phonemes is limited in expressive potential, lacking full grammar, but no primate (or any other mammal or bird, for that matter) species are that limited in their vocal tracts.

Some have suggested that human phonetics evolved to distinguish tribes from each other. But since each tribe can geographically only have a limited number of neighbouring tribes, and contact with more tribes beyond that requires peaceful contacts that would favour mutual understanding as opposed to language confusion, hundreds of phonemes are certainly overkill for that function too.

The choking hazard of the human vocal tract may simply be as nonadaptive as the small hearts of lions that makes them easily exhausted.

How to sound like an ape
To sound like an ape, you should not only "ooh-ooh" when you exhale. You should instead "ooh" one time for each inhalation and one time for each exhalation, and breathe rapidly. For gorillas, that is. For chimpanzees with their higher pitch, you should "iih" instead of "ooh", but the same applies otherwise.