How to solve this sound problem (minimum sampling rate required)

[Physicsfan2379]

Summary: The problem:

If one wants to make a digital record of sound such that no audible information is lost, what is the longest interval, Δt, between samples that could be used? ( it gives a hint that humans can hear sound waves in the frequency range 20 Hz to 20 kHz. It should be a very simple question but I don't know what does the "longest interval" mean here)

Δt

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[DaveE]

In other words, how fast do you have to record data points to reconstruct the sound without information loss below 20KHz. Fs = 1/Δt where Fs is the sample frequency, Δt is the time between samples.

 

[Anand Sivaram]

That is what is given by Nyquist Shannon Sampling Theorem.
https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

 

[Klystron]

The problem statement just mentions recording; i.e, audio data collection. Playback requirements and engineering technology limitations can also help determine initial sampling rates, frequencies and filters. Analogies/examples come to mind:

Suppose a biologist wants to record bird vocalizations in the wild with limited resources. Pre-filtering unwanted audio signals such as crickets, wind and moving water would reduce storage requirements among other benefits.

Suppose an engineer knows beforehand that they need to synchronize video and audio recordings. The video playback frame rate has been chosen for realistic motion ~30 frames/second. Recording audio signals that vary at faster rates could have benefits but the video playback rate provides a "ballpark figure" to help choose audio data collection parameters.