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Absolute dB (SPL, etc.)
Sometimes you will see dB used in special situations to represent absolute values. The dB is still a ratio, but it is used with different standard references. For example, dBV uses 1 volt as a reference, and dBm uses 1 milliwatt.
In audio work dB SPL refers to Sound Pressure Level, which uses a reference of 0.0002 microbar RMS. (A microbar is a unit of pressure equal to a millionth of standard atmospheric pressure.) 0 dB SPL is approximately the threshold of hearing at the most sensitive frequency of the average normal human ear. (See "Formulas For Working With Sound".)
Consider that the average ear can hear up to about 120 dB SPL before pain begins. This requires a million times more voltage to produce than 0 dB, which seems to imply that an ideal digital audio system needs at least 21 bits to capture the full range. (20 bits = 2^20 = 1048576, but we need to handle both positive and negative voltages, so we would need twice that range, or 21 bits.)
Luckily, we rarely listen in "threshold" conditions with zero background noise, and we rarely want to bring ourselves to pain, so the theoretical 96 dB range of a 16-bit system is usually adequate for most purposes.
Besides absolute values like dB SPL, you may see some that are "semi-absolute", like dB SL (Sensation Level) or dB HL (Hearing Level). In these cases the reference level is a subject's own threshold for detection, using some particular protocol.
Let's say you are studying the ability to detect small amounts of frequency modulation in brief tone bursts. You want to know if the ability to do this varies with loudness. Before you begin, you determine the minimum level of an unmodulated burst that a subject can just detect, and call that 0 dB. Then you run all your modulation tests at levels of 20, 40, 60, and 80 dB above this subject's reference level.
You repeat this whole procedure for each subject. Note that each may be using different absolute sound levels, since each may have a different threshold of hearing. This method tends to compensate for those differences, but note that it also has a really big benefit regarding ease of operation: There is no need to make sound level measurements. You simply adjust the signal level to find the reported threshold, read that level setting and call it 0 dB, and add the needed dB to get each test level.
Of course, it would be best if you also recorded the actual SPL, using a calibrated setup. But even if you do not have a calibrated microphone (yet!), you should still record the actual absolute settings as a way to determine the approximate absolute thresholds of your subjects. This will help you spot those with serious hearing problems that may need to be excluded from comparisons. And then when you eventually get a calibrated mic, you may be able go back to that data and convert the settings to approximate SPL.
(A good but inexpensive calibrated reference microphone is the Dayton Audio iMM-6, under $20.)
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