www.paformusic.info Decibels

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Contents

• Introduction
• Three Important Things
  1. A Relative Measurement
  2. A Logarithmic Measurement
  3. A Power-related Measurement
• About Sound Levels

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Introduction

The decibel (abbreviation dB) is usually thought of as a unit for specifying the level of an audible sound, but this is only one of its many uses. In particular, in PA work it is also used for specifying the level of an audio signal. This unit is frequently misunderstood, and a full and accurate understanding requires some detailed explanation, which this page provides.

The decibel is so-named because it is one-tenth ('deci-') of a larger (and very rarely used) unit − the Bel. The Bel is a term which originated in the telecommunications industry as a name for the proportional reduction in voice signal power that occurred per mile length of a standard telephone line. It was named after an inventor of the telephone, Alexander Graham Bell.

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Three Important Things

There are three important things to understand about the decibel:

1. It is a relative measurement.
2. It is a logarithmic measurement.
3. It is a power-related measurement.

These are explained in more detail below.

1. It is a relative measurement.

Values specified in dB provide a comparison − they always indicate the difference between two levels.

dB values are often used to specify the amount of change in level. In such cases the dB values tell you nothing at all about how large or small the signal levels are. For example, a dB value may specify:

• The extent of a rise or fall in level occurring over some time interval, at one particular point in a system. We are comparing the present level with the level at an earlier time.
• The extent to which a signal's level is increased (gain) or reduced (attenuated) as it passes from one point to another through the signal chain. We are comparing the level at some specified point in the chain with the level (of the same signal) that is present (at that time) at a specified previous point.
• The effect of moving a fader, or changing the setting of any other type of level control or gain control. e.g. if you move a fader from its '−15' marking to '−10' then you have increased the level by 5 dB.
• The amount of cut or boost provided by an equaliser (EQ), at a specific frequency or (approximately) over a specific band of frequencies. We are comparing the post-EQ level with the pre-EQ level, at that specific frequency or in that specific frequency band.
• The slope of an EQ curve or crossover curve. For example, a high-cut slope of 18 dB/octave means that (above the crossover frequency) signals at a particular frequency are attenuated by 18 dB more than those at half that frequency.

The smallest change in level that can be perceived by the human ear is somewhere between 1 and 3 dB (depending on the conditions and on the listener), while a change that sounds like "twice as loud" requires an increase of around 10 dB.

For calculations on purely relative levels, try these relative level converters.

However, although the decibel is fundamentally a relative measurement, dBs are also frequently used to specify actual levels. This is made possible by the use of standard reference levels − the level to be specified is compared with the appropriate standard reference level, and the difference between the two is expressed as a value in dBs. In order for such dB values to be meaningful, it is essential that in each and every case it is clear what the applicable reference level is. This is because the quoted dB value only indicates the extent to which the specified level is higher or lower than that particular reference. For example, a level specified as 0 dB means a level equal to the reference level, a level of 15 dB is a level 15 dB higher than the reference and a level of −8 dB is a level 8 dB lower than the reference. So the reference level that is being used must be stated in each case − or at least must be unambiguously implied. Standard references are typically indicated by a letter (or letters) appended to the abbreviation 'dB'. The most common examples of this are dB SPL, dBV, dBu, dBm, dB FS and dB TP (the links are to details below). Programme loudness is also measured on a decibel scale relative to a standard reference − see LUFS.

• dB SPL − indicates decibels relative to a reference sound pressure level (SPL) that is just at the threshold of human hearing (that is, the level at which sound becomes just audible). Decibels relative to this reference level are used when specifying the level of an audible sound at a particular location. For example, a 2 kHz sound at a negative dB SPL level cannot be heard at all, one at 0 dB SPL can barely be heard in even totally silent surroundings, and one at 130 dB SPL would be painfully loud. Note that quoted sound levels relate to the location of the measurement, which may be some distance from the sound source. Levels closer to a source are likely to be higher − how much higher depends on the nature of the source and on how sound is propagating from it to the measurement location (see, for example, Inverse square law). See About Sound Levels below for further information.
  
  However, we cannot simply fix the 0 dB SPL reference as "the threshold of hearing", because that is not a clearly defined level of sound pressure − the sensitivity of the ear varies from person to person and is very dependent upon the frequency of the sound. (The threshold of hearing is at an SPL some 50 dB higher at 100 Hz and some 10 dB higher at 10 kHz, as compared to its value at 2 kHz.) To enable SPL values expressed in dB to have a clear meaning, an agreed standard reference pressure level is needed, and this is fixed at a value of 20 µPa (= 200 pbar) RMS regardless of frequency. (This value of SPL corresponds to a 'sound intensity level' (SIL) of 10⁻¹² watts per square metre − but SIL is a measurement not usually encountered in PA work.)
  
  To take into account the different sensitivity of an average human ear at different frequencies, standard 'weighting curves' have been agreed. The most common of these is the so-called 'A' curve. SPL measurements that apply this curve, and so give an indication of the loudness that would be perceived by an average listener, taking into account the various frequencies present in the sound, are described as 'A-weighted' measurements. These are usually designated 'dB (A) SPL' or as just 'dB (A)'. (Note however that neither of these is a formally recognised designation − the strictly correct form is 'L_A = x dB', where 'x' stands in place of the value.) 'dBA' or 'dB A' should never be used, as the 'A' does not indicate a reference level. ['dBA' has sometimes in the past been used to indicate 'decibels Acoustic' i.e. decibels relative to the 20 µPa SPL reference, unweighted, but this is no longer recognised usage because of the potential confusion with the use of 'dB (A)' to indicate an A-weighted measurement.] There are also 'B' and 'C' weighting curves − for details see Weighting.
  
  This is fine if we want to indicate the sound level at a particular location, but what if we want to indicate the sound level produced by a particular sound source (under specified conditions)? As the sound level will decrease with increasing distance from the source and will probably also be affected by direction, we would need to specify the distance of our measurement (usually 1 metre) and its direction (usually 'on-axis') along with the sound level. (See Sensitivity.) For a point source in free space, the sound level decreases by 6 dB for every doubling in distance (see Inverse square law). For a line source such as a line array, within the source's critical distance the level decreases by 3 dB (in free space) for every doubling in distance.
  
  

  dB SPL value converter:

  Enter the known value in the relevant left-hand box and click '=' to get the converted value.

• dBV − indicates decibels relative to one volt RMS. Decibels relative to this reference level are often used when specifying the voltage level of a signal provided at an output of an item of equipment, or expected at an equipment input.
  
  When specifying an output level, a complication arises in that the voltage provided by the output will inevitably depend to some degree upon the impedance of the load to which it is connected (if any). Therefore, there will be some uncertainty about a quoted value of output signal level unless the load impedance at which that level applies is stated (or implied). For example, the output level (sensitivity) of microphones is usually specified with the output unloaded. In practice, however, the use of voltage-matched interconnections means that in most cases analogue audio output levels will be affected relatively little by any loads likely to be connected to such outputs in normal use.
  
  The nominal average programme level used for line-level interconnections between most semi-professional equipment, home studios, etc. is −10 dBV (0.316 V). The levels used by professional equipment are more usually expressed in dBu. To convert a value in dBV to a value in dBu, just add 2.2 dB.
  
  dBV value converter:
  Enter the known value in the relevant left-hand box and click '=' to get the converted value.

• dBu (formerly dBv in the USA) − similar to dBV, but indicates decibels relative to 0.775 volts RMS rather than to one volt RMS. As the 'u' stands for 'unloaded' (or 'unterminated'), this measurement strictly only applies to an output when it has no load (or termination) connected. In practice, however, analogue audio output levels are usually affected relatively little by the connection of normal loads (see Voltage-matched). So, in practice, dBu is also used to specify connected output levels, and to specify the levels expected at equipment inputs.
  
  The reason for using a reference level of 0.775 volts is that this is the RMS voltage level required to produce an average power of 1 mW in a load of 600 ohms impedance. (This impedance value is used for historical reasons − see dBm below.) But note that the 0.775 V reference level is always used for levels specified in dBu, regardless of the fact that in the vast majority of cases the impedance at the point of measurement will not in fact be 600 ohms (with the result that a level of 0 dBu will in practice not result in a power transfer of 1 mW at that point).
  
  The nominal average programme level used for line-level interconnections to most professional equipment is +4 dBu (1.23 V). The levels used by semi-professional equipment are more usually expressed in dBV. To convert a value in dBu to a value in dBV, just subtract 2.2 dB.
  
  dBu value converter:
  Enter the known value in the relevant left-hand box and click '=' to get the converted value.

• dBm − indicates decibels relative to one milliwatt (mW). Decibels relative to this reference level are sometimes used when specifying the level of a signal provided at an output of an item of equipment, or expected at the input of an item of equipment.
  
  It is sometimes encountered in the specification of optical interfaces, where it is used to specify the optical power level that is produced or required by the equipment.
  
  Confusion frequently surrounds the use of this measurement because, in the world of PA systems, it has sometimes been misused. As the reference is a power level (rather than a voltage level), a level expressed in dBm specifies, strictly, that the indicated power is actually flowing from a source to a load. In practice however, what is frequently meant is that such a power would flow from the source if a load of 600 ohms impedance (a standard impedance figure for impedance-matched analogue audio line systems) were connected and the voltage of the signal were unaffected as a result.
  
  In other words, in such cases dBm is being used to indicate the voltage level (rather than the power level) of the signal, against a reference that is the voltage level required to produce an average power of 1 mW in a load of 600 ohms (i.e. 0.775 volts RMS). This is strictly an inappropriate usage, but sadly is often encountered − the correct designation for a decibels measurement of voltage against a reference of 0.775 volts RMS is not dBm but rather dBu.
  

• dB FS − indicates decibels relative to the maximum possible instantaneous sample level that can be represented in the particular digital format in use, e.g. by a digital audio signal or within an audio data file. This maximum level is called the 'full scale' value, which is the reason for the abbreviation 'FS'. So it can be seen that dB FS relates to instantaneous peak levels, and that positive values of dB FS are not possible. Any instantaneous value of a signal, at the input of an analogue to digital convertor, that would cause 0 dB FS to be exceeded (i.e. would give a positive value of dB FS) will result in clipping during conversion to digital form (see Analogue to digital conversion). So, the nominal (peak) level in decibels relative to the 0 dB FS reference (always a negative value) is a direct indication of the available digital headroom.
  

• dB TP (true peak) − indicates a dB FS value that has been adjusted upwards, by software, to take into account the likely actual peak values of waveform crests that fall between the present sampling intervals. These actual peak values may become relevant during later digital processing, for example during sample rate adjustment. As with dB FS, the reference is the maximum possible instantaneous sample level that can be represented. Ensuring that a signal level remains below 0 dB TP ensures that, during such a later adjustment, clipping is unlikely to occur (without needing to reduce the overall level of the signal).

2. It is a logarithmic measurement.

This means that each extra decibel does not indicate that the existing level has increased by a certain amount, but that it has increased by a certain proportion or ratio. (Expressed as a percentage, each dB represents approximately 26% increase in power, or 12% increase in voltage). So, the greater the existing level, the more the actual increase that is indicated by each additional decibel. Likewise, of course, the greater the reduction that is indicated by each fewer decibel.

The main reason for this method of measurement is that this is how the ear responds to sound pressure levels (i.e. loudness), and adopting this scheme means that a value of level change expressed in dB relates directly to how much the sound level is perceived to have changed.

Further advantages of a logarithmic measurement are:

• Enabling the convenient representation of widely differing values, without having to use very large or very small numbers − for example see About Sound Levels below.
• Enabling the cumulative effect of successive gains and losses throughout a signal chain to be calculated by addition rather than by multiplication.

(For the mathematical meaning of logarithm, see Log.)

3. It is a power-related measurement.

Clearly this does not mean that decibels is only ever a measurement of actual power, as we have already explained that it can be used to specify a voltage level. Rather, it means that the numbers used in a decibel value are always indicative of the (relative) power level that would be obtained from the level being specified, if given a chance. The benefit of this is that a decibel figure always conveys the same meaning in terms of (relative) effective power levels − regardless of whether it is used to refer to a voltage level, an electrical power level or a sound pressure level.

So, given two power levels, the number of decibels representing the difference between them is calculated as 10 times the logarithm (to the base 10) of their ratio. Given a number of decibels, the equivalent ratio of power levels is calculated by dividing the number of decibels by 10 and finding 10 raised to that power. It can be useful to remember that a doubling in power level is represented by an increase of almost exactly 3 dB.

However, if we are working with voltage levels rather than power levels then a modified version of the equation applies, because power is proportional to the square of the voltage (providing that the impedance remains constant). In terms of decibels, a squared value is represented by simply twice the number of decibels. So, given two voltage levels, the number of decibels representing the difference between them is calculated as 20 (rather than 10) times the logarithm (to the base 10) of their ratio. Similarly, given a number of decibels, the equivalent ratio of voltage levels is calculated by dividing the number of decibels by 20 and finding 10 raised to that power. It can be useful to remember that a doubling in voltage level is represented by an increase of almost exactly 6 dB.

The 'voltage' version of the equations also applies to conversions between decibels and ratios of sound pressure levels (e.g. ratios of values measured in µPa or pbar), because sound power (or intensity) is proportional to the square of the pressure level, in a similar way to which electrical power is proportional to the square of the voltage level. So given two sound pressure levels, the number of decibels representing the difference between them is calculated as 20 times the logarithm (to the base 10) of their ratio. Given a number of decibels, the equivalent ratio of sound pressure levels is calculated by dividing the number of decibels by 20 and finding 10 raised to that power.

Relative level converters

Ratios:
Enter the known value in the relevant left-hand box and click '=' to get the converted value(s).

Changes in level:
In the converters below, enter known values in the two left-most boxes on the relevant line and click '=' to get the converted value.

Power changes

Voltage changes

Pressure changes

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About Sound Levels

The typical approximate sound pressure level (SPL) of some everyday sounds are given below. Note that sound levels are quoted at the location of the listener, and will be affected by the listener's distance from the respective source (see Inverse square law). As well as dB SPL, the corresponding SPL in µPa and Pa is also indicated, to illustrate the much greater convenience of measurements in decibels (see also the SPL value converter).

Exposure to high sound levels can cause permanent damage to hearing, so it is important not to exceed safe limits. It is vital to understand that the damage from small amounts of exposure adds up over time. So, in terms of hearing damage, exposure is not just a matter of sound level, but also of the duration involved and of how often the exposure is repeated.

For example, an exposure to a level varying between 90 and 100 dB (A) (after taking into account any hearing protection worn) for 2 hours once in a while may not be a problem for most people. However, this exposure may cause significant damage if repeated on many occasions, as further damaging exposure worsens any damage caused previously. For public events, check the current Health and Safety legislation on sound exposure limits applicable in your country or district. Legal exposure limits are often quoted in terms of a continuous steady level that would give the same total sound energy dosage − see L_eq. The L_eq limits for staff may differ from those for audiences, e.g. due to different exposure times.

Maximum peak levels may additionally be stipulated, because extremely loud sounds can cause permanent hearing damage even if the duration of exposure is extremely short − e.g. a pyrotechnic detonation. No person should be exposed to sound at levels above 140 dB (A) without appropriate hearing protection, no matter how short its duration.

Also remember that exposure to high sound levels does not require high power levels, if the sound source is very close. For example, sound levels of 85 dB SPL or more are easily obtained from the earphones of most personal music players, and frequent lengthy exposure to such levels may well be sufficient to cause permanent hearing damage. Similar considerations of appropriate use apply to headphones or in-ear monitoring devices worn by sound crew or performers.

Further guidance on avoiding damaging levels of exposure can be found on the UK website Sound Advice. Advice for employers in the UK is provided by the HSE leaflet 'Noise at Work', INDG362. (External links, open in a new window.)

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This page last updated 16-Jul-2019.