Sound Playback Rate?

We're working on a modern reconstruction of the phonautograph, the first machine to record sound (in 1857), updated to use Snap! We created a prototype strip chart recorder that draws a graph of a soundwave sent to it from Snap!:

We would like to record the sound at a higher sampling rate and then play it back at a slower sampling rate (which will enable us to reduce the chart speed and capture finer detail in the waveform).

We found that the lowest apparent rate at which a sound can be played back is about 3,000 samples for second. Is there a technical reason for this limitation? Is there a workaround that would enable us to play a sound back at a rate of even fewer samples per second?

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