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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!)

1Just reading the other posts and that seems to be the consensus. It's like you're not playing back a smooth sine wave because of the sample rate, you're actually playing back a stepped sine wave, and it's these steps which create the extra harmonics - because they're like square or sawtooth waves depending on the shape and distance. I think recording the output (at 48khz sample rate) and looking at it in a waveform editor would explain what you are actually hearing. – Mark Durham – 2013-11-09T11:00:01.903

"Can I run the Mathematica code easily?" Yes, if you don't mind to download and install it. (It's free for 30 days, and the

`Play`

function is available since version 2 and hasn't change since version 6. )…… Oh, you've managed to recreate it? Then it's not necessary :) , and it'll surely help if you post the video! – xzczd – 2013-11-09T11:44:42.463Finally I managed to climb over the GFW to watch the video 囧. That's a good demonstration. Then, how to explain the position of the shrieks? Why are they obvious only at peaks and valleys of sine wave? – xzczd – 2013-11-09T13:42:44.300

I don't think I'm hearing it like that, I believe it's on the up and down sections of the wave - where there is more change. It is a bit difficult to see in the video as the sync is slightly off - good old YouTube. – Mark Durham – 2013-11-09T14:29:43.077

Oh, and now I know what GFW stands for - must be so frustrating – Mark Durham – 2013-11-09T14:47:01.227

After watching your video, I came up with an idea to check the position of the shrieks with some mathematica code(I've added it to the post in mathematica.se), and I should admit that I've misheard the position of the shrieks 囧. Thanks for your video!

– xzczd – 2013-11-11T09:16:44.590Pleased it helped. And thanks for the cross post - we should all do more of that now we're part of Stack Exchange. It's interesting to see different approaches to the same problem from varying fields. – Mark Durham – 2013-11-11T10:39:00.733