Why don’t different notes create acoustic beats? Why is it when two different notes are played in unison an acoustic beat is not heard, but when they same note slightly out of tune is played beats are heard?
 A: In music, 'unison' usually means the SAME note, so musically spoken, it is not possible to play two different notes in unison, by definition. I assume with 'unison' you mean 'at the same time', but maybe there is some misunderstanding here.
However: Let us think of two notes as the pure root note/base frequency, which would correspond to pure sine/cosines. If you add two of them with a different frequency, the combined function will have an envelope that is also a sine/cosine, with a frequency that is the difference of the frequency of the two notes. If the two notes are very close such that it is below the frequency we as humans can hear, you will hear an acoustic beat, since you actually here how the amplitude modulates over time. If the difference between the two notes is within the frequency range we can hear, you will hear a third note.
So, if you hear the SAME pure frequency twice, perfectly in tune, there will be no acoustic beat. If you have the same note twice, slightly out of tune, you will have an acoustic beat. Two different notes that have a difference that is audible as a tone, you should hear a third note.
Keep in mind that notes played on actual instruments have a lot of higher harmonics with different amplitudes (or in case of something like bells and cymbals a lot of non-harmonic higher frequencies) you hear at the same time. This complicates the set-up and also changes how easily you hear the acoustic effects we are talking about here.
Still, the effect with the third note can be produced on real instruments, and it is easier the less harmonics the instruments have: If two people playing a recorder can each hold a high pitched note, you can hear a low note added. With this principle organ pipes have been built that made it possible to hear lower notes than the physical length of the pipes corresponded to. I add that this effect is much harder to reproduce with instruments with a lot of higher harmonics and if the intonation is not constant.
A: The hair cells in your ears cannot instantly respond to the different frequency components in a sound that you hear. It takes time (IDK how many milliseconds) for them to respond. If the period of the "beats" is significantly less than the time it takes for a hair cell to start or stop resonating, then you will only perceive continuous tones.
It's similar to what happens in your eyes if you look at a flashing light: If the frequency of the flashing is great enough, then you only perceive a steady glow.
