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The relationship between the objectively measured amplitude of a sound and our subjective impression of its loudness is complicated.
Our sense of the relative loudness of two sounds is related to the ratio of their intensities, rather than the mathematical difference in their intensities.
For example, the relationship between a sound of amplitude 1 and a sound of amplitude 0.5 is the same to us as the relationship between a sound of amplitude 0.25 and a sound of amplitude 0.125. The subtractive difference between amplitudes is 0.5 in the first case and 0.125 in the second case, but what concerns us perceptually is the ratio, which is 2:1 in both cases.
Does a sound with twice as great an amplitude sound twice as loud to us?
In general, the answer is "no". Our subjective sense of "loudness" is not directly proportional to amplitude.
The softest sound we can hear has about one millionth the amplitude (or intensity) of the loudest sound we can bear. Rather than discuss amplitude using such a wide range of numbers from 0 to 1,000,000, it is more common to compare amplitudes on a logarithmic scale.
The ratio between two amplitudes is commonly discussed in terms of decibels (abbreviated dB).
A level expressed in terms of decibels is a statement of a ratio relationship between two values—not an absolute measurement. If we consider one amplitude as a reference which we call A0, then the relative amplitude of another sound in decibels can be calculated with the equation:
$20 \times log_{10}(\frac{a}{a_0})$
Note: 1 decibel is the just noticeable difference (JND) in sound intensity for the normal human ear.