It appears to just be a carrier signal alternately transmitted and not transmitted. As the carrier is in the MHz range, the audio cannot be a direct mapping of that frequency. I don't know the specific mechanisms used to make the signal audible as a particular tone, or whether that tone would differ between different receivers.
There are multiple recordings of it on http://www.dd1us.de/spacesounds%201.html. While a few have varying pitch, they don't appear to repeat (and not over 4 beeps). To my ear any variation in pitch sounds more like the variances you hear when trying to tune in a signal. Most of the recordings have only a repeating tone. I suspect that your second video is just a repeated loop of four particular tones.
One of the audio files contains some contemporary analysis by someone at Caltech.
For the first three days, both signals were beeping -- that is the carrier was alternately switched on and off. And it appeared that when one channel was on the other was off.
It is our personal opinion that these signals contain no telemetering, or at most a low accuracy telemetering of simple information, and that the beeping was for purposes of easy identification.
Per wikipedia, the duration of the "on" signal could be modified by temperature and pressure information. I couldn't find any sources that countered the assertion that the carriers were fixed and not (intentionally) modulated within the craft other than the sub-second transmitting/not transmitting periods.
Another contemporary paper (Guier and Weiffenbach , "Theoretical Analysis of Doppler Radio Signals from Earth Satellites," Nature 181 , pp. 1525-1526 (1958). ) describes the signal capture this way:
We had one distinct advantage over other groups: one of us was
completing a Ph.D. dissertation in microwave spectroscopy and had a
high quality communication receiver and the necessary understanding of
how to make precision frequency measurements. Because of the fortunate
happenstance that the Beltsville, Md. WWV 20-MHz standard broadcast was
at nearly the Sputnik frequency, the output from the receiver could be
made to be the audible difference between the WWV standard and the
Our first reception of the Sputnik seemed only a momentary triumph
when we realized that there was no telemetry on the 20 MHz signal,
just a pure tone that at first appeared to wander in frequency by a
surprisingly large amount. After about 5 minutes, it was unmistakably
clear that the wandering was the moving Sputnik's Doppler shift, which
we were by then recording with precise frequency and time information.
That said, if the reported frequencies were accurate, the difference would be .005MHz or 5kHz. While very audible, 5kHz is a pretty high tone. None of the recordings I listened to seemed to have tones that high. So I suspect a different method was used in general