That's not jitter or modulation. That's adding a 3 kHz tone.
Here is my 2nd attempt of building a thought experiment, concerning a worst case DAC-clock jitter scenario which could turn an inaudible signal into something unwanted audible.
Just assume a high level ultrasonic, but inaudible signal being converted from digital to analog in a DAC.
In case, when the DAC clock is not clean in terms of jitter, there will be a phase modulation of the a .m. ultrasonic signal.
Further assuming that this jitter is periodic at 24KHz (not a mandatory frequency, just as an example - it might be related to a 48KHz sampled test file and therefore associated to the internal DAC´s oversampling rate running at nx48KHz...).
Aiming at the worst case of detecting such jitter by ear, one could use an inaudible high level ultrasonic test signal at e.g. 21KHz.
That jitter would (also) cause an audible 3KHz beating tone (24KHz - 21KHz = 3KHz, see also below), when the jitter is high enough.
3KHz was targeted, because the ear is most sensitive in that range.
Just like to repeat that this is a theoretical scenario, trying to determine some spec boundaries for an unquestionable DAC-clock, without having all the measuring eqt. available...
Further assuming you have a nice stereo, which is capable of generating some 105-110dB of max. SPL in your listening position, that 3KHz tone may become audible above -110dB below electrical full scale of the DAC (top notch ears required, mine probably less good performing...).
Now here comes the improved thought experiment´s idea how to calculate a boundary jitter value.
Periodic jitter can be seen as a phase (or frequency) modulation, where fortunately some pre-solved equations can be applied.
I used these nicely explained ones from the University of St. Andrews in Scotland:
https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part12/page1.html
This case relates to narrow band frequency modulation math, i. e. a small modulation-factor Beta, but with a high modulation frequency in this case (I found no mathematical reasons, why this shouldn´t be applicable).
For a small Beta, the crucial Bessel function factors determine the amplitudes of the "carrier frequency" (which shall be the test signal - becomes 1) and the "difference tone" (which represents the 3KHz tone - becomes Beta/2).
Beta divided by 2pi x testfrequency equals to a peak jitter value. From there onwards -110dB of the beating tone amplitude equal to 1/316K fraction of the ultrasonic test signal. This factor equals to the a. m. Beta/2 amplitude, resulting in peak jitter of 42ps, which is about 30psrms.
Considering a typical jitter performance from a crystal oscillator (e. g. a TCXO) in the range of 1 to a few ps @ 100MHz (assuming the well discussed ESS9018 DAC chip clock), it is well below practical audibility.
If you leave the listening position and come really close to the speaker, you are able to hear that tone at much lower levels (maybe a factor of 20 or more), that´s why I think so called femto-second clocks are discussed and marketed...and also why Amir mentoned that DAC clocks should be as close as possible to the DAC-chip, because any foreign electric or magnetic field will induce addtional jitter.
In addition to the pure clock jitter, one can assume that the dividers in the DAC chip also cause jitter. Therefore digital chip design appears to be at least as important as the clock jitter itself. I didn´t design DA-converters so far (with the exception of a 50Hz DAC to control motor speed of my Thorens TT), but I guess that high speed synchronous on-chip dividers and careful chip layout are essential...One interesting thing seems to follow, i. e. the higher the DAC´s clock frequency, the less jitter may be expected.
Hope I got the assumptions and the calc right this time!
Actually, when playing a -20dB full range sine wave sweep on my old TEAC VRDS-10 CD-player, one can hear a very quiet beating tone, when the sweep frequency has already become inaudible, wonder if this relates to this effect? My SPDIF-driven ESS9018-based DAC stays clean at ultrasonic, when playing that 16/44 file!
One late remark,
I have to correct myself, regarding the beating tones heard on my old Teac VRDS-10, which are also audible, with same intensity, using the 9018-based DAC via Toslink.
Utilising the same measurement CD with an external CD-drive on the PC-based player does not exibit these beating tones.
So the measurement CD and the DAC seem to be clean.
The next suspect would be Sony´s CXD2500AQ signal processor in front of the Toslink output and the internal DAC...
This finding also relativises the old (and widespread) claim, improving such an old CD player by adding an external DAC...
