The Dreaded Decibel - Part 2

Now we've got to grips with the principles behind the decibel as a unit, let's look at how we use it in the real world for recording and sound engineering.


Here are some voltages corresponding to typical dBu levels used in audio

Voltage Ratios (dBu)
dBuvoltage ratioRMS voltspeak volts
-200.100 0.0770.109

The dBu reference is 0.775 volts RMS (average). The peak values in this table assume the signal is a sine wave (a pure tone), which has a peak value of 2√2×RMS. Although it's a legacy of largely obsolete telephony technologies, the 0 dBu reference is important for digital recording as most digital signal processing (DSP) chips used for audio have a maximum input level of 1 volt. Minus one dBu is thus a safe maximum signal level into an audio DSP chip, assuming a sinusoidal waveform.

Sound pressures

Here are some real-world sound pressures expressed (approximately) in dB SPL

Sound Pressure Levels (dB SPL)
dB SPLpressure ratiopressure (SPL)typical sound
01.002×10-5 Pa
auditory threshold, mosquito at 3 metres
103.1626.32?10-5 Pa
quiet rustling of leaves
20102?10-4 Pa
recording studio
3031.626.32×10-4 Pa
unoccupied room in countryside
401002×10-3 Pa
quiet library
50316.26.32×10-3 Pa
normal conversation
601,0000.02 Pa
typical TV
8010,0000.20 Pa
busy road, long term hearing damage
9450,1191.00 Pa
microphone performance reference level
100100,0002.00 Pa
pneumatic drill at 1 metre, rock concert
12010620.0 Pa
short term hearing damage
1303.16×10663.2 Pa
threshold of pain
1503.16×107630 Pa
jet plane at 30 metres
18010920,000 Pa
physical destruction of ear tissues
1945×109105 Pa
most powerful possible sinusoidal sound wave

Absolute sound pressures (SPL) are expressed in pascals (Pa) RMS. A pascal is equal to a hundred-thousandth (1/105) of standard mean atmospheric pressure (a fraction over 1 bar). RMS (Root Mean Square) is a way of averaging a varying signal so as to represent its effective mean power. For a sinusoid, 194 dB is the highest attainable mean sound pressure. Its negative peaks reach 0 bar (total vacuum). Above this SPL, continuous sound waves cannot exist. They "clip" on their negative excursions because a pressure of less than 0 bar is physically impossible. Only shock waves (single travelling pressure fronts) can exceed this sound pressure - but they're not really worth listening to and you're unlikely to survive the experience of encountering them.

Digital audio and dynamic range

Decibels referred to digital full scale (dBFS) are used to describe the maximum range of representable digital values of a recording or playback system. Here are the decibel equivalents of the standard bit depths used in digital audio and compared with a couple of real world auditory ranges (highlighted). The "loudest" reproducible level in a digital recording - the largest number that can be represented by the number of digital bits available - is always referred to as 0 dB, and the "quietest" reproducible level (equivalent to a value of zero) by -n dB, where "n" can be determined from this table.

Important Digital Full Scale Ranges
dB Rangedescription
32 bit data range: ±2 billion
24 bit data range: ±8 million
max. safe auditory range
16 bit data range: ±32768
max. instantaneous auditory range

These figures are of critical interest, as there is currently much debate about whether the 16 bit data format of the Red Book music CD standard is adequate. Many pundits try to persuade us to move to 24 or even 32 bit digital formats, suggesting that a dynamic range - the ratio of the loudest recordable sound to the quietest - of more than 90 dB is necessary for realistic music reproduction. But it's not at all clear we need to - for playback anyway. Human hearing has a massive overall dynamic range - some 110 dB even if we take care not to cause pain or damage. But not all of this is available instantaneously. We have a "sliding window" about 65 dB wide that moves up and down the total range, accommodating to average sound levels with a response time in the range of from 5-30 seconds to (in extreme cases) several hours, depending on the degree and rate of change in average level. This means that if you're playing a track that reaches a level of 80 dB SPL, any part of the track that falls below 15 dB SPL for a only couple of seconds may seem silent.

So although we can adapt to sounds throughout the whole 110 dB range, it's not all available to us instantaneously. The 65 dB instantaneous range is a lot less than that offered by a CD. But even disregarding this physiological limitation, to make use of the whole of the maximum 96 dB range of a CD, with the quietest sound on the CD at the threshold of hearing the loudest would be roughly equivalent to that of a pneumatic drill a couple of metres away. This is unlikely to be conducive to a comfortable listening experience.

There are other reasons for increasing bit depth - particularly when recording and editing - but the CD standard remains a pretty adequate playback standard for those of us with normal hearing. One of the reasons this debate has surfaced, however, is failure to recognise how poor is the quality of many "consumer" CD players, which undermines the inherent quality of the CD recording. Another is the tendency for record labels to over-compress popular music CDs, reducing the dynamic range drastically by pushing everything to the loud end. Some notable examples have only 40 or so dB actual dynamic range - the lower 50 dB of the available range being almost completely devoid of recorded information. Now a dynamic range of 40 dB is definitely too restricted, but that's not the fault of the Red Book standard, but of the recording engineer, who's only using a well under one per cent of the available dynamic range of the medium. My wild soundscape recordings typically have a dynamic range of 65 dBFS RMS (about 70 dBFS average peak), leaving a safe 25 dB to handle occasional transient peaks without overloading the digital range.