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Decibels

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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.


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 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      Pa     
 
   Pa      dB SPL  

   dBV      V     
 
   V      dBV  

   dBu      V     
 
   V      dBu  

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:

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

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 ÁPa 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).
  dB    power 
ratio 
  and   voltage or
pressure
ratio 
  
 
  power
ratio  
   dB    
 
  voltage 
ratio  
   dB    
  pressure 
ratio  
   dB    

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
   W   changed by   dB      W new level   
 
   W   changing to   W    dB change

Voltage changes
   V   changed by   dB      V new level   
 
   V   changing to   V    dB change

Pressure changes
   Pa   changed by   dB      Pa new level   
 
   Pa   changing to   Pa    dB change


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 ÁPa and Pa is also indicated, to illustrate the much greater convenience of measurements in decibels (see also the SPL value converter).

dB SPL Description SPL
    ÁPa Pa
0 Barely audible (near-silence) 20 0.00002
20 Whisper 200 0.0002
40 Quiet office background 2,000 0.002
60 Everyday conversation, ringing telephone 20,000 0.02
70 Restaurant background noise 63,250 0.06325
80 Heavy city traffic, alarm clock 2 ft away 200,000 0.2
90 Motorcycle, workshop tools, lawn mower 632,500 0.6325
94 The SPL at which microphone sensitivities are usually quoted 1,000,000 1
100 Chain saw, pneumatic drill 2,000,000 2
110 Dance club (peak) 6,325,000 6.325
120 Rock concert (peak), thunderclap 20,000,000 20
130 Jet taking off, gunfire, max SPL for some microphones 63,250,000 63.25

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 Leq. The Leq 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 14-Jun-2019.