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I work as a sort of multi-purpose engineer/developer at a very small startup game company. Recently, I've been asked to help out with audio development and editing, and I've been mostly able to hold my own.

One thing I'm not very familiar with, though, is sample rates. I understand what they are, and I know that 44100 Hz is considered a sort of default because it's CD Quality.

What I want to know is if there's a sort of practical peak, where the human ear can no longer hear the difference. In graphics development, they say that the human eye can't see the difference above 60 Hz (although some people are starting to say 75-90 Hz, I think). Is there a similar limit in audio development?

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The sample rate of audio and video are two different things.

Video's Frames Per Second (fps)

In video, a frame (sample) rate of 24fps is required to prevent flickering. The common frame rates (25 and 30) has to do with the fact that early televisions used the mains frequency for the purpose of syncing (50Hz in the UK, 60HZ in the States). The primary reason for higher frame rates is the reduction of motion blur. To my knowledge, latest research suggests that somewhere between 90Hz-112Hz the effect is no longer recognisable.

Audio's Sample Rate

The sample rate of digital audio relates to the highest frequency captured/reproduced. As the Nyquist Theory states:

A signal can be perfectly captured and reconstructed, so long the signal is band limited and sampled at equal intervals at a frequency at least twice the highest frequency present.

Thus, a 44,100Hz sample rate can accommodate a signal with frequencies up to 22,050Hz. A 40000Hz sample rate can accommodate a signal with frequencies up to 20,000Hz

Following a debate, the 44,100 Hz figure was chosen as the best compromise between various requirements, including those of the various television standards at the time. This sample rate was subsequently used with audio CDs.

However, analogue-to-digital conversion (ADC) technology in the 1980s still exhibited distortion at levels that could be reduced using higher sample rates. Thus, when the DVD standard was established, the sample rate of 48,000 was chosen; representing a higher-fidelity audio.

The limitations in technology at the time are no longer part of modern ADC, where nearly all converters use 1-bit oversampling.

Human Hearing Range

The audible human hearing range is quoted as 20Hz - 20,000Hz (20kHz). Not a single empirical experiment in history has shown that any human being is capable of hearing frequencies above 20kHz. This is attributed to the density of the high-frequency 'hair' cells in our ears and the maximum rate at which they fire.

It is also worth noting that about more than half the population above the age of 45 is incapable of hearing frequencies above 16kHz.

Inaudible Frequencies can Yield Audible Ones

However, any signal being converted from digital to analogue must pass through a non-linear system before it reaches our ears. The obvious example of such system is the speaker cone. When audio passes through a non-linear system, distortion is created in the form of additional frequencies. Under such conditions, frequencies above 20kHz can actually result in distortion below 20kHz. However, unless the non-linear system is fundamentally faulty, for programme material (normal typical everyday sounds - not a loud sin wave of 30kHz) the distortion created is inaudible.

The same principle applies when digital audio is processed in a non-linear fashion within a digital system. Distortion content above 20kHz will be generated, and depending on the sample rate, it may alias back to the audible range.

The last two paragraphs explain why it is sometimes justified to use sample rates higher than 44,100.

ADC Frequency Headroom

To answer your question directly, the required limit of sampling rate (while only accounting for human hearing) is 40,000Hz.

However, before sampling, convertors need to filter audio content above 20,000Hz. Since the effect of all filters is gradual (they cannot simply remove everything above a particular frequency, they only attenuate it gradually), convertors need some headroom to sufficiently remove content above 20,000Hz. Thus, a sample rate higher than 40,000Hz is always required.

Conclusion

While 40,000Hz represents the theoretical max sample rate required with humans, ADC technology still requires some headroom above this figure.

With modern ADC technology, 44100Hz is perfectly capable of capturing material up to 20,000 Hz.

From a game development point of view, you should not worry about this aspect.

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For final delivery, some have argued that going much over 44,100 is actually bad ( evolver.fm/2012/10/04/…) However this excellent answer is correct to point out that higher sample rates can be justified durring production. –  Bjorn Roche Sep 19 '13 at 17:54
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The range of human hearing is typically 20-20K Hz if I remember correctly, and this is why CD audio was set at 44100. To properly reconstruct a signal, you need to have approximately 2x the sample rate of the maximum frequency (see: Nyquist-Shannon sampling theorem). 44100 was picked as a value that gave acceptable quality reconstruction within the file storage budget they had at the time (~750MB for an album)

Frequencies outside the human-hearing range can still interfere constructively and destructively to color the audible frequencies, so people (at least informally) suggest using equipment which can handle such frequencies. This would be the reason why 48K and 96K are used: they can capture a wider range of frequencies.

side note: the CMYK print standard for images is usually quoted as 300dpi and this is because it is 2x the 150-line screens used for plate making in high-quality print publications. Again, sampling rate twice the frequency to avoid artifacts and moire.

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+1 great description of the correlation between human hearing and sampling rates. –  Byte56 Sep 19 '13 at 15:54
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