Sound is a mechanical vibration of a medium in the hearing range.
A medium can be practically anything: a gas, a liquid or a hard material. Most commonly we perceive sound propagation in the air, where it travels with the speed of 343 m/s at the room temperature (20°C). The speed varies with temperature, but in the human habitat's thermal range, that's not a big variation (a couple of percent).
Some aircraft can reach the speed which is higher than the speed of sound (343 m/s= 1,235 km/h), also called the supersonic speed. Some other phenomena in the nature can reach that speed, such as meteorites entering the Earth's atmosphere, There are also scientific speculations about the fact that some dinosaurs were able to move their tail with the ultrasonic speed, generating intimidating sounds.
The speed of sound is different in different media: for example, in water, this parameter is 1,484 m/s, while for iron it is 5,120 m/s, again, both at the room temperature.
The basic shape of a pure uniform oscillation is a sine wave. This is what we use as a basic signal shape in sound, too, especially in electronics. This is the shape that we use for most measurements to test the behaviour of sound equipment.
This signal is defined by two parameters:
amplitude (A), which is directly connected with the loudness, therefore how loud or quiet the sound is, and
frequency (f), which determines the pitch of the sound - it tells us how many times per second a sound vibrates.
The signal makes its full turn when it equally passes positive and negative half-period creating a full cycle.
The time needed for this signal to terminate a full cycle is called a period (t0) or wavelength and it is measured in seconds. Frequency determines how many periods are completed in one second. The unit for frequency is 1/s or, more commonly, Hertz (Hz).
For example: if a signal oscillates with a hundred periods in a second, that's 100 Hz.
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