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Question 1: Here are two facts that I know about CD quality audio:

  1. Audio is sampled to 16 bits at a rate of 44.1 kHz
  2. The bitrate is 1411 kbps.

I can't quite work out the math.

$ \frac{16\ \text{bits}}{} \times \frac{44.1 k}{sec} = \frac{705.6\ \text{kbits}}{sec} $

which does not equal 1411 kbps. Why?

Question 2: I remember my EE professor telling me that 44.1 kHz is the highest frequency that humans can hear. Why, then, do some online music services offer "high resolution" streams or files that are recorded at 96 kHz or even 192 kHz? Can only people with mutant-level hearing take advantage of those sampling rates?

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  • $\begingroup$ Are you sure you're seeing "96 kHz" and "192 kHz"? Far more likely is 96 kbps and 192 kpbs (kilobits per second) since these are common AAC/MP3 encoding bitrates. $\endgroup$ – Eric Towers May 7 at 23:37
  • $\begingroup$ @EricTowers: Look at this offer page from the Qobuz music streaming service. It clearly says: FLAC 24-Bit up to 192 kHz. qobuz.com/us-en/music/streaming/offers . Also Amazon Music HD: Up to 24-bit / 192 kHz amazon.com/music/unlimited/why-hd $\endgroup$ – stackoverflowuser2010 May 7 at 23:50
  • $\begingroup$ These are both marketing copy. I'm fairly jaded about the technical accuracy of marketing copy. For instance, I clearly recall ads for computers having 0.064 bits of memory. ("64 mb".) Maybe this is an analog sampling rate, but I would bet a quarter it's the codec bitrate. $\endgroup$ – Eric Towers May 7 at 23:57
  • $\begingroup$ @EricTowers: Here's a Sony DAC that Supports PCM 32bit/768 kHz electronics.sony.com/audio/audio-components-turntables/… $\endgroup$ – stackoverflowuser2010 May 8 at 0:15
  • $\begingroup$ @EricTowers we are pretty sure we are talking about 96 kHz and 192 kHz PCM streams, at up to 24 or 32 bits per sample. No codecs involved. $\endgroup$ – Justme May 8 at 13:06
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What is missing from your calculations is that it requires a multiplier of two because CD quality audio is two channels for stereo. 2 * 44.1 kHz * 16 = 1411.2 kbps

The answer to your second question is twofold.

First of all, human hearing range is typically said to go up to 20 kHz, not to 44.1 kHz. However to sample data up to 20kHz, it needs to be sampled at above 40 kHz, and to have some margin for various reasons (analog reconstruction filters among others), CDs use 44.1 kHz sampling rate.

Second, indeed, there is no technical reason to transfer mastered audio recordings to consumers at higher rates than 16-bit 44.1 or 16-bit 48 kHz, as humans do not have the auditory sensors to receive frequencies past 20 kHz. The reason these high-resolution streams exist is purely marketing and demand.

However, in the studio it can make sense to record and store intermediate tracks at higher resolution before the final downmix. And even when playing back 48 kHz streams, typically modern DACs first digitally upsample the sampling rate to allow for better audio quality with cheaper analog filters.

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    $\begingroup$ "to sample data up to 20kHz, it needs to be sampled at least at 40 kHz" -- This should be "needs to be sampled at more than 40 kHz (i.e. fs>40k, not fs>=40k)", otherwise it's implied that 40 kHz is enough, but that will get you a net zero if the samples fall on the crossing points. $\endgroup$ – a concerned citizen May 7 at 8:02
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    $\begingroup$ @concernedcitizen Thanks, I updated. I could have also written "up to but not including 20kHz" but it does not matter much which around it is. For the human ear it makes little difference if it is <= 20kHz or just < 20 kHz, but it is important to convey the theory right. $\endgroup$ – Justme May 7 at 8:30
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    $\begingroup$ I've always assumed that the 20 kHz figure for the upper frequency limit of human perception follows some kind of normal distribution so that the number of people who can hear sounds beyond that threshold decreases quickly. If that's true, there may still be quite a few who'd benefit from 48 kHz or even higher sampling rates. Is there a physiological limitation that that sets a hard cut-off point to the upper limit of human frequency perception? $\endgroup$ – Schmuddi May 7 at 8:41
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    $\begingroup$ @Schmuddi the 20 kHz number is simply good enough for a commonly stated value. Babies can hear above that and adults less, so there is considerable variation among individuals. Compared to 44.1 kHz, 48 kHz is not used to get higher frequencies up to 24 kHz, it is to have a larger transition bandwidth from passing 20 kHz to filtering 24kHz which allows for less costly filters. $\endgroup$ – Justme May 7 at 10:18
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    $\begingroup$ @stackoverflowuser2010 it most likely isn't, and they're just tricking themselves. Audiophiles are generally not the most scientifically rigorous group of people. I wouldn't trust anything they say unless it's backed by some kind of blind trial $\endgroup$ – llama May 7 at 15:36

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