# How to solve this problem involving the “longest interval”?

The problem is shown as follows:

If one wants to make a digital record of sound such that no audible information is lost, what is the longest interval, $$\Delta t$$, 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)

• – PM 2Ring Jul 31 '19 at 7:43

## 1 Answer

An analogue audio signal is shown in blue. You are required to take samples (instantaneous values) of the signal at regular intervals of time to produce a "copy" of the analogue signal.

You will note from the diagram that the greater the sampling rate (the less the sampling interval) the more faithfully the sampled copy reproduces the original signal.

As the period of the original signal gets smaller the rate of sampling has to increase to get a good reproduction of the original signal.
So in essence you are being asked how many samples are need per period to get reasonable reproduction of the original signal and hence what is the time interval between these samples?