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Amplitude is a measure of the maximum air pressure variation from a standard of zero air pressure. There is a strong correlation between the amplitude of a waveform and the perceived intensity of the sound. This means that there is a correlation between the amount of air displacement generated by a sound generating system, and the perception of its intensity, or loudness.
However, in order for a sound to be perceived by human hearing, its amplitude must exceed some minimum. This is referred to as the threshold of audibility. The threshold of audibility is the threshold above which a disturbance of air pressure can be heard as sound (as opposed to some other sensation). The threshold of audibility is amazingly low: about 1/billionth of one erg. Just to provide some context: an erg is a measure of energy required to lift an object with a weight of one milligram a quarter of an inch off a surface.
However, the correlation between amplitude and perceived loudness is not exactly linear: other factors play a large part. For instance, there is a correlation between perceived loudness and pitch. The so-called Fletcher-Munson curve reflects empirical data showing that, basically, sounds with low frequencies (between 40 and 100 Hz), or high frequencies (above 5 kHz) require higher amplitudes in order to be perceived as having the same intensity as sounds with frequencies in between these two extremes.
Another factor contributing to the perceived loudness of a sound is timbre. A sound that has spectral energy only within a thin band (like the tone produced by a pure tone) will sound less loud than a sound of similar amplitude but with richer spectral components. Other psycho-physical factors contribute to perceived loudness, including the musical or environmental context of the sound.