Let's say you have a 26000Hz sound and a 22000Hz sound. You'd hear a 4000Hz (26000 - 22000) beat (audible) faintly.
No you wouldn't. For the ear to hear a beat frequency it must be able to hear both tones. So if you had two sine waves with frequencies of 15kHz and 25kHz, you will not hear an additional 10kHz tone you will only hear a single 15kHz (providing you are able to hear up to 15kHz).
Things get even more complicated when you add in more sounds, that even if not audible, will still form a beat
The beat is always lower in amplitude (volume) than either of the two tones. So if you can't hear one of the two tones, you definitely can't hear the beat frequency.
To delve even deeper, the timbre of the instrument doesn't go at a straight tone, it varies depending on instrument, this is why you can tell instruments apart. Since they change constantly, so do the beats.
No, you are mixing up two totally different audio processes. A single note played on an instrument does not produce a single audio frequency, it produces a fundamental and then a range of harmonics at different frequencies, the balance of all the harmonics gives the instrument it's timbre and is how you can tell a trombone from an electric guitar even if they are playing the same note. Harmonics are a different phenomenon and not directly related to beat frequencies.
Beat frequencies can only be produced by non-linear devices, like amps and synths. If you create a beat frequency in a synth, say you modulate a 25kHz and a 15kHz wave, you will get a 25kHz wave, a 15kHz wave and a 10kHz wave. If we record this using a 96kHz sample frequency and our amp and speakers are capable of replaying the 25kHz wave, what we would hear is a 15kHz wave and a 10kHz wave. If the amp or speakers only have a frequency response up to 20kHz then the 25kHz signal will not be reproduced and all we would hear would be a 15kHz wave and a 10kHz wave (unless the 25kHz signal has caused the amp or speakers to distort!). If we record the synth output at 44.1kHz sampling rate, the 25kHz wave will be filtered out by the anti-alias filters and what we would hear is a 15kHz and a 10kHz wave. Anyone spot the difference between these three? .... Good, because there isn't one!
So what's the use of extending beyond 20000Hz? You get cool beats.
No you don't. There is no benefit to extending beyond 20kHz!
I've heard the argument of can we hear over 20kHz many times over the last 20 years or so. The answer is NO, there is nothing above 20kHz which you can hear. In fact, unless you are a young child, there is probably nothing above 16-17kHz which you can hear and if you're in your 50s you are probably down to 12-13kHz. If there are signals above 20kHz which affect other frequencies in the hearing range then we can record, reproduce and hear those interactions but we can never hear the ultrasonic frequencies themselves. Also consider that even a high C on a piccolo flute is only 4.2kHz pretty much everything above this frequency is just harmonics of generally diminishing amplitude.
The other argument I've heard is that we might not be able to hear beyond 20kHz but maybe we can perceive it somehow. Sure, this is easy. Say I played a 30kHz sine wave at you at 200dB. Your skin would peel away from your body and a fraction of a second you would be dead but for that fraction of a second I'm pretty sure you would "perceive" 30kHz!!
You have to also consider that none of the common studio recording microphones are capable of capturing frequencies above 20kHz and most speakers also dramatically roll off after 20kHz. So it's very unlikely you could find many recording which contained anything but noise above 20kHz anyway.
Having said all this, there is a potential benefit to recording at 96kHz sampling frequency. It is easier (read cheaper) to create good quality filters inside the converters using higher sample frequency. There is a point of diminishing returns though, a sample rate of 192k has more noise and distortion than the 96k sampling rate. Recordings made on high quality professional converters at 44.1k still provide the highest level of audio quality.
G