What controls the MAXIMUM allowed frequency of the sound in electronics? The circuit or the speaker component?
Those are available sampling rates, not maximum frequencies of the audio signal. Sampling rates imply a maximum audio signal frequency of less than half of the sampling rate – but that's just an upper limit. You, as a human, can't hear beyond 20 kHz, usually (lab-condition experiments suggest you might hear loud tones above that, but that's irrelevant to normal volume audio reproduction).

The maximum reproducible audio frequency might also be limited by analog things (your speakers not going higher than say 20 kHz), and by the filtering of the digital-to-analog conversion stage, and the filtering inherent to your amplifier.


  what actually causes these limits?


Depends. The fact that these devices have a discrete set of available sampling rates is a matter of convention: What would it help you if one of your devices supported say 50 kHz, but none of the others? Seems like a nice, round number, but doesn't help you.

That's why 44.1 kHz and 48 kHz are so common: They have been used in commercially successful storage media and that "seeped" into end devices. For example, 44.1 kHz was simply the rate that the CD uses – and hence it becomes so standard (and the CD uses it because some previously existing studio technology used it). 48 kHz is a studio standard by the AES (Audio Engineer Society), and hence what a lot of studio equipment "naturally" uses.

Technically, sampling rates above 48 kHz definitely don't make sense; you can't hear things above 24 kHz, so storing or transporting them is of no benefit to a system. (Whether or not you need more than 44.1 kHz at all: I personally doubt it matters, but there's people with strong opinions and untested hearing on that...)

The reason hardware isn't built to support arbitrary rates is that it's actually hard to


Generate arbitrary oscillators of high reliability (at least historically – gotten way better the last 15 years)
Coordinate and convert between arbitrary sampling rates rather than between a limited set of them. You need resamplers – and a good rational resampler is typically lower-complexity than a comparable good arbitrary one.


The fact that your equipment supports multiple sampling rates at all is probably to 


ensure compatibility and
out of "we have it anyway in our silicon".


Notice that these restrictions don't apply very much to software-based signal processing: Your computer doesn't care whether your signal is sampled at 48 or 96 kS/s; it's just a sequence of numbers to the computer. The latter rate only means that it has to process twice as many samples per second, and that filters of the same steepness are twice as long, typically, meaning you quadruple your CPU load. That might not be a big deal for your PC dealing with only few sample streams at once, but it becomes intense in large studio settings, telephony applications with thousands of participants or when you're trying to make a digital hearing aid work on a coin cell for more than a day.