This is the sampling theorem. You start with a continuous band-limited signal (e.g. sound pressure [0], low-pass filtered such that there is essentially no content above 20kHz [1]). You then sample it by measuring and recording the pressure, f_s times per second (e.g. 48 kHz). The result is called PCM (Pulse Code Modulation).

Now you could play it back wrong by emitting a sharp pulse f_s times per second with the indicated level. This will have a lot of frequency content above 20kHz and, in fact, above f_s/2. It will sounds all kinds of nasty. In fact, it’s what you get by multiplying the time-domain signal by a pulse train, which is equivalent to convolving the frequency-domain signal with some sort of comb, and the result is not pretty.

Or you do what the sampling theorem says and emit a sinc-shaped pulse for each sample, and you get exactly the original signal. Except that sinc pulses are infinitely long in both directions.

[0] Energy is proportional to pressure squared. You’re sampling pressure, not energy.

[1] This is necessary to prevent aliasing. If you feed this algorithm a signal at f_s/2 + 5kHz, it would come back out at f_s - 5kHz, which may be audible.