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The dB scale


The frequency  range of audible sound is nominally 20Hz to 20kHz (a ratio of 1:1000), and people with normal hearing can perceive an amplitude range of sound pressure between the threshold of hearing (tex2html_wrap_inline46409, i.e. micropascal) and the threshold of perception of 1:1000000. To reduce this large range of physical values to a smaller range of numbers the decibel (dB) scale  was introduced.

The dB is not an absolute measuring unit. Rather it is the ratio of a measured value to a fixed reference value. The sound pressure level   (SPL) in dB, indicated as dB-SPL, uses a logarithmic scale with the threshold of hearing defined as 0db:


where tex2html_wrap_inline46419. With every multiplication of the sound pressure P by the factor 10, we add 20dB to the sound pressure level:   200tex2html_wrap_inline46423 corresponds to 20dB, tex2html_wrap_inline46425 corresponds to 40dB etc. By using decibels, the range of 1:1000000 is mapped onto a range from 0dB to 120dB: 120dB-SPL may be emitted by aeroplanes during take-off, and the range of speech is between 30 and 70dB, with normal conversation (1m separation) at 62dB.

In the case of two sound sources, the logarithmic scale means that the power levels in dB cannot be simply added to get the resulting level. While, for instance, 90+96 and 97+97 add to 97 and 100db, respectively, the sum approximates to the larger value alone if the two levels differ by more than 10dB.


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