Can binaural beats be generated with carrier tones outside the audible frequency range? I know that binaural beats are a controversial subject, as they might not work for everyone. In my own tests on myself I shuffled multiple recordings of binaural beats, with stereo headphones on, not looking at the frequency and resulting brain state advertised by each. I did, in fact, experience notably different mind states in these tests. 

Binaural beats can be generated using carriers at any frequency within the audible range of human hearing. The frequency of binaural beats dictates the mind state that is being induced.


I'm wondering if binaural beats can be generated using carrier tones outside the range of human hearing?
And suppose that that works, do these binaural beats still have an effect on the state of mind? In other words, can you entrain your brain without being able to acoustically perceive the carrier tones producing the beats?
Short answer
No, infrasonic or ultrasonic sound cannot generate binaural beats. 

Background
Binaural beats are generated in the brain and are associated with the frequency bands of the EEG. Binaural beats in the delta (1 to 4 Hz) and theta (4 to 8 Hz) ranges have reportedly been associated with reports of relaxed, meditative, and creative states, and used as an aid to falling asleep. Binaural beats in the alpha frequencies (8 to 12 Hz) are said to enhance alpha brain waves and those in the beta frequencies (16 to 24 Hz) have been associated with reports of increased concentration or alertness (source: Web US). 

The binaural beat is not heard in the ordinary sense of the word - the human range of hearing is from 20-20,000 Hz and hence pretty much all the aforementioned frequencies cannot be registered directly by the auditory system. Instead, binaural beats are auditory brainstem responses which originate in the superior olivary nucleus of each hemisphere. They result from the interaction of two different auditory stimuli from opposite ears. The carrier frequencies have to be approximately below 1000 Hz and have to differ in frequency between one and 30 Hz. For example, if a pure tone of 400 Hz is presented to the right ear and a pure tone of 410 Hz is presented simultaneously to the left ear, an amplitude modulated standing wave of 10 Hz, i.e., the difference between the two, is experienced as the two wave forms mesh in and out of phase within the superior olivary nuclei (source: Web US). 

Because auditory information needs to be sent to the brainstem, the auditory system is needed from the far periphery up to the brainstem. Thus, the hair cells in the inner ear are necessary to convey the information to the brain via the auditory nerve. Because infrasonic and ultrasonic sounds do not activate the hair cells and do not lead to auditory nerve activity, these sounds can hence not activate the brainstem and do not generate binaural beats.

Sources
- American Speech, Language &amp; hearing Association
- Gray, Auditory System: Structure and Function. In: Neuroscience Online
- Web US