From the definition „sound is a mechanical vibration of a medium in the hearing range“, we have already covered a part of a medium, but „what is the hearing range“?
The hearing range is the range between the lowest and the highest audible frequency. For a human, this is between 20 Hz and 20 kHz (20,000 Hz). Different animal species have different hearing ranges. For example, a mouse can hear from 1 kHz to 100 kHz and a chicken from 125 Hz to 2 kHz.
Now we have covered the whole definition of sound: we know what a medium is and how the speed of sound behaves in it, and we know what the hearing range is.
Previously we have said that a sound/signal is defined with two parameters: frequency and amplitude. As there is a definition for the hearing range in frequency, there are also limits in amplitude: what is the quietest sound we can hear and what is the loudest sound we can bear?
The amplitude range for a human hearing is defined between 0 and 120 dB, where 0 dB is the „loudness“ of breathing, and 120 dB is a threshold of pain.
dB is not really a unit, but a logarithmic way to define a ratio between a reference signal and a measured signal.
0 dB means that the ratio between a reference and a measured signal is 1:1, while 120 dB is 1:1,000,000, therefore we can't bear the sound that is a million times louder than our breathing. Another interesting ratio is 6 dB (1:2).
Just to give you a real life example of what dB means as a noise:
0 dB – minimal perceivable sound
30 dB – whisper
60 dB – conversation
98 db – hand drill
115 dB – loud rock concert
120 dB – pain threshold
140 dB – jet engine
180 dB – death of hearing tissue
In music notation, we use two extremes for the loudness definition: ppp (pianississimo, which equals to whispering) and fff (fortississimo, equal to yelling).