How do certain frequencies of sound induce psychological states? As one example, a specific low frequency beyond our hearing perception can make people feel nauseous and even vomit.

I'm sure there are more documented studies surrounding the correlation of auditory induced states, but how and/or why does this occur?

Also, does this phenomenon happen to deaf people as well?
Auditory information is conveyed to the brain from the cochlea via the VIII cranial nerve (aka vestibulocochlear nerve). Under standard conditions the vestibular system gets activated when we move our heads. If we spin around rapidly this can obviously make us feel dizzy and nauseous. The vestibular system can also be activated do to other causes. For example, positional alcohol nystagmus (aka the drunk spins) occurs due to alcohol changing the densities of the endolymph and the cupula (part of the sensory organ in the semicircular canals). It turns out that low frequency pressure waves at high enough levels can activate the sensory cells in the vestibular system.

In some causes of deafness and hearing loss the vestibular system remains normal, or near normal. These individuals are therefore susceptible to these feelings. Other causes of deafness destroy the vestibular system making individuals immune to these feelings.