Why I hear shrieks that have the same pitch as sample rate when the frequency of the signal is very small?

Usually, human can't hear sound with a frequency lower than 20 Hz, but what's confused is, some very slight shrieks generate after I sampled a 1 Hz sine wave with a high sample rate.

To be precise, the shrieks are around the position of peaks and valleys of sine wave, and the frequency of the slight shrieks seems to be equal to the sample rate i.e. a 1 Hz sine wave with a sample rate of 2000 will generate 2000 Hz shrieks. (Remember to regulate volume since the shriek is really slight. )

This question was first posted in mathematica.SE but hasn't got a satisfactory enough answer yet, since this seems to be a "multidisciplinary" issue, I'd like to post it here(not migrate it!) , too. The original question has used some mathematica code, so I've tried to re-express it in a more general way. (I think the original is also understandable even for guys who don't know mathematica, click here to read the original post and answer it if you want!)