You're welcome, I'm glad that was helpful. And sample repetition is assumed by a lot of people, don't feel dumb. It doesn't make intuitive sense to use zeros and make the sine wave (that most people imagine the process with) look discontinuous. If you want a deeper, but relatively intuitive view of sampling, check out my series here:
Sampling theory, the best explanation you’ve ever heard
As far as increasing the sample rate, it doesn't change any frequencies. But since the "Fs", the sampling frequency was raised, sidebands that were a result of the sampling process are now in the new, wider audio band. (By "audio band", I mean everything below half the sample rate.) So, we need to clear everything but the original signal with a lowpass filter.
OK, some might have a little problem with the idea that things go on forever, but remember we're just doing math, where things are pure. The same happens in analog sampling, but pulses are imperfect and the images die out as frequency response droops—it still works because we plan to eliminate them with a lowpass anyway. Perfect impulses have no limit to their frequency content, real impulses do. But by keeping only one reading per sample and discarding the rest of the analog waveform, we simulated a perfect impulse. Just saying this to prep for the fact that PCM is a form of amplitude modulation (AM, like the radio), with a perfect impulse, therefore sideband copies—plus and minus—exist mirrored around multiples of the sample rate. And any changes to the part that's in the audio band changes those images as well. We get rid of the images in converting back to analog. So, if we start with a lowpass filtered audio signal that ends up with this bandwidth:
View attachment 220634
After sampling, we have this in the frequency domain:
View attachment 220635
Note that that the original band is "mirrored" around Fs (and 2Fs, and 3Fs...), it's reversed below it, and is the forward but shifted in frequency above it.
If we zero-stuff to up the sample rate, the result is this—we only changed where Fs is:
View attachment 220636
But note that if we look at the new audio band, that below half Fs, we have those mirrored images. They are ultrasonic, but if we run that through a DAC at the higher rate, those frequencies will be in the analog output.
To get back to the audio we started with, we just lowpass filter (again, this and all processes are mirrored) to keep the audio below half the original rate:
View attachment 220638
If you wanted to play this out a DAC with 20 kHz audio bandwidth, even a very gentle filter will work great—it just needs to ensure the red part is removed.