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Say I was sampling a sound incorrectly and it produced a constant signal as below:

enter image description here

What would this signal sound like? In Matlab, it plays nothing. Is this correct?

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  • $\begingroup$ Probably. It's aliased. $\endgroup$ Apr 30 '14 at 0:56
  • $\begingroup$ Great answer man thanks!!! I wasn't aware that all aliased signals were heard as nothing when played!!!! $\endgroup$ Apr 30 '14 at 1:03
  • $\begingroup$ No, not all aliased signals are heard as nothing, but ones in which they alias down to DC frequency will. Admittedly I neglected to mention that, but that's because I thought it was obvious. $\endgroup$ Apr 30 '14 at 1:40
  • $\begingroup$ That's why to perfectly reconstruct a signal you have to sample at at least twice the frequency. See this question for related information: physics.stackexchange.com/q/90433 $\endgroup$ Apr 30 '14 at 3:12
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Matlab's silent output is correct. Physically, sound is a fluctuation of the molecules in some medium. If your waveform is perfectly constant, it corresponds to constant pressure: no fluctuations, meaning no sound. If it's very nearly constant, you will probably still be unable to hear the corresponding pressure wave without the aid of significant amplification.

Edit: In response to the quick comments above, an aliased signal is not generally silent, only in the extreme case when the wave is sampled at the same level each time. More typical undersampling will just result in a different sinusoid with possibly different amplitudes or frequencies than your original, thus the name "aliasing": the sampling process gave some new "name" to the original wave.

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  • $\begingroup$ First good answer I've had on this exchange for ages. Thanks mate. I was being sarcastic in my above. He's very ignorant. $\endgroup$ Apr 30 '14 at 1:30
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Admittedly this isn't really physics-related, but I found something amusing in Mathematica when trying this:

Play[Sin[8000 2 Pi t], {t, 0, 2}]

enter image description here

Mathematica by default samples Play at 8KHz, so it just gets floating-point aliasing noise when it's told to sample an 8KHz note (which it then gleefully amplifies to an audible level, resulting in something which is remarkably stupid-sounding).

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  • $\begingroup$ Please delete your incorrect comment and off-topic answer. Regards. $\endgroup$ Apr 30 '14 at 1:37
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    $\begingroup$ I clarified the comment I left under your question. "nshaffer" already posted the complete answer, so I posted this answer for supplementary amusement purposes. $\endgroup$ Apr 30 '14 at 1:44
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    $\begingroup$ Also, it does answer the question, just indirectly. $\endgroup$ Apr 30 '14 at 2:13
  • $\begingroup$ Wish I could test this "stupid-sounding" sample, but alas no Mathematica & WolframAlpha doesn't understand 'play.' Oh well. $\endgroup$
    – Kyle Kanos
    Apr 30 '14 at 12:32
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This should sound like a sine wave.

However if your cycle is too long, it is not audible to the human ear. To be audible, the cycle should be over 20Hz, or 20 times a second.

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