acoustics - If two sound waves that are different frequencies create beats that occur several hundred times per second, can you hear this effect as its own tone?

If you have multiple waves of different frequencies, the interference from the different waves cause "beats".

(Animation from https://en.wikipedia.org/wiki/Group_velocity)

Let's say that a green dot in the above animation reaches your ear a few hundred times per second.

Is it possible to hear this phenomenon (wave groups occurring at frequencies in the audible range) as its own tone?

Answer

No, one cannot hear the actual beat frequency. For example, if both waves are ultrasonic and the difference in frequency is 440 Hz, you won't hear the A (unless some severe nonlinearities would come into play; edit: such nonlinear effects are at least 60 dB lower in sound pressure level).

When two ultrasonic waves are close in frequency, the amplitude goes up and down with the beat frequency. A microphone can show this on an oscilloscope. But the human ear does not hear the ultrasonic frequency. It is just silence varying in amplitude :)

(I know a physics textbook where this is wrong.)

Edit: in some cases the mind can perceive the pitch of a "missing fundamental". For example, when sine waves of 880 and 1320 Hz are played, the mind may perceive a tone of pitch A. This is a psychoacoustic phenomenon, exploited for example in the auditory illusion of an Escher's staircase.