Sound as data: sampling rate and amplitude

Digital sound is a sequence of numbers. A microphone measures air pressure many times per second. The number of measurements per second is called the sampling rate (Hz). A CD uses 44 100 Hz. A standard phone call uses 8 000 Hz.

Each measurement is the amplitude at that moment. The value lies between −1 and 1 (or −32768 to 32767 at 16-bit resolution). Higher amplitude means louder volume.

Why is 44 100 Hz enough? Humans hear up to about 20 000 Hz. According to the Nyquist theorem, the sampling rate must be at least double the highest frequency to be reproduced. At 8 000 Hz (phone), high frequencies like 's' sounds disappear, resulting in a darker sound.

import math
fs = 8000                 # samples per second
f = 440                   # note A (Hz)
sekunder = 0.5
n = int(fs * sekunder)    # 4000 samples
vag = [math.sin(2 * math.pi * f * i / fs) for i in range(n)]
print(len(vag), round(max(vag), 2))   # 4000 1.0

A higher note (e.g. 880 Hz) produces twice as many oscillations per second. If you halve the amplitude (0.5 * sin(...)) the sound becomes quieter. Adding two waves element-wise gives you a chord.