The right tool for sound level measurement
How do professionals measure volume? Decibels are commonly used in both everyday speech and the audio industry, but are often misunderstood. Decibel units are established in professional audio engineering, noise control, acoustics research, linguistics, communications engineering and numerous other disciplines. We light up the dark. And in advance: In certain places, we deliberately simplify it. This article is about a pragmatic understanding that is not intended to replace a study of acoustic phonetics.
A decibel classifies the sound pressure level of a sound source in everyday life
A decibel is one tenth of a bel. The unit is named after Alexander Graham Bell. However, the bel unit is very large for measurement purposes and accordingly too broad and imprecise. That is why a tenth of a bel has prevailed as the unit, indicated by the prefix deci (Latin for tenth). The decibel was first used as a scientific unit of measurement in 1924 when Bell Laboratories developed the “Bel Scale,” now colloquially known as the decibel scale.
An increase in the sound level by 3 dB usually corresponds to a doubling of the sound pressure (i.e. the strength of sound waves). We have the following exemplary orientation values for “volume”, as measured on the decibel scale:
20 decibels is approximately a ticking clock.
30 decibels are sounds of breathing and soft whispering.
40 decibels is a quiet yet not whispered conversation.
The noise coming from most refrigerators are between 35 and 45 decibels.
80 decibels is loud screaming; from this level on, continuous sound exposure becomes unhealthy. Most vacuum cleaners are about that loud as well.
100 decibels is the approximate volume of chainsaws or trucks driving close by. That's roughly the threshold of discomfort – things get unpleasant from here on. This is however subjective and is also a matter of (unhealthy) habits. Because most dance clubs are around 100 decibels loud.
The decibel scale expresses a logarithmic ratio
Now things will get a bit abstract: There is no absolute sound pressure level that is referred to as a decibel. A decibel value is always relative to something.
Unfortunately, when specifying a decibel value, we often have no indication of what it refers to. For example, if the output of a mixer reads -10 dB, that usually means it is 10 dB below 0 dB. However: This also means that 0 dB quite simply merely means that the sound pressure is neither increased nor decreased. Perhaps you already have an idea of what this is all about:
“0 dB” is not silence – that's a common misconception. 0 dB is the human auditory threshold and describes a sound pressure of 0.00002 Pascal (20 µPa) at 1000 Hz. If 30 dB is a low whisper, that refers to the minimum audible noise (0 dB).
The difference between linear and logarithmic
When we speak of metres, the distance between 5 metres and 6 metres is the same as the distance between 76 metres and 77 metres. So, a metre is a linear scale.
Decibel is logarithmic, which means that: The increase from 80 decibels to 81 decibels is much larger than the increase from 7 decibels to 8 decibels. The higher the value itself, the higher the difference between two decibel values.
If you're having a hard time imagining this right now, think of a square. If you extend the sidelines, it gets bigger and bigger. The larger the square is, the greater the increase of the inside area. To put it in mathematical terms (and use it at the next party): The logarithm is the inverse of the exponential function.
Why does the decibel have to be such a complicated scale?
Because we have good ears. A linear scale (like for watts or volts) for volume would have to be very extensive, i.e. run from 0 to at least five digits. The pain threshold at very high volume is about a million times greater than the barely audible threshold of hearing. Such measuring scales are rarely used for good reasons. They make measurement methods and calculations very complicated.
Decibels make calculations easy, but …
… underneath the surface, the decibel is difficult to understand as a unit because people are unaccustomed to thinking in logarithms as well as ratios without a classic zero point. A decibel value alone is meaningless if it is not related to something. This is inconvenient, since it is almost never used in this way in everyday practice. A pragmatic solution would be this: When the decibel value is not explicitly stated, the implied all-important reference is usually 0 dB. A mixer's mic input might state -50 dB, which would mean that it's 50 dB lower than 0 dB. A mixer's line output might show -10 dB, meaning it's 10 dB lower than 0 dB.
What is 0 dB if it isn't silence?
In simplified terms, 0 dB is the reference level. It's the level to which most decibel readings you read anywhere refer to. If the measured level is neither above nor below the reference level, the level difference is zero, so our reference level is called 0 dB. But what does the reference level mean? In most situations in the field of audio, 0 dB refers to the nominal level, for example from a mixer. The nominal level is colloquially mostly the “line level”.
Level vs. dB: Decibel is an auxiliary unit of measurement for the complex sound pressure level
To understand this, we need to define the term sound pressure level (SPL for short, sometimes just: sound level). The sound pressure level is measured using a (measuring) microphone in Pascal (Pa). It basically boils down to nothing more than measured pressure fluctuations. Sound pressure is the difference between the pressure of a sound wave and the ambient pressure of the room through which the sound is propagating (usually atmospheric pressure). At this point, we will save ourselves the in-depth side trip to the realm of atmospheric background and different frequencies. The sound pressure level, which is a very complicated value on closer inspection, can be translated into the more easily processed decibel scale in acoustics and electrical engineering. The sound pressure level is therefore also a logarithmic variable with a fixed reference value (so we're back to the human hearing limit, 20 µPa at a frequency of 1000 Hz).
The sound pressure level in decibels for a sound of pressure amplitude P is given by the following relation:
LP = 20 log (P/P0)
Note that the equation still has one undefined variable in the equation, namely P0. This shows once again that decibels are a relative measurement scale. In this case, the measured sound pressure amplitude P is determined relative to the value P0. P0 is the hearing threshold at 1000 Hz.
Pressure amplitude is a measurement of the strength (amplitude) of sound waves. It indicates how much the pressure of sound waves deviates from atmospheric pressure. Atmospheric pressure is the pressure exerted on the earth by the weight force of air. The pressure amplitude of a sound wave is measured in pascals (Pa) and is a direct measure of the sound energy emitted by a sound source. The pressure amplitude of a sound wave is proportional to the sound intensity and the acoustic power. A higher pressure amplitude means the sound wave has more energy and is therefore louder. However, the pressure amplitude of a sound wave decreases along with the increasing distance from the sound source because some sound energy is lost due to absorption and attenuation by the environment. Pressure amplitude is often used to evaluate speaker performance or the impact of noise on the environment. It can also be used to study the vibrations of structures such as bridges or buildings that are caused by sound waves.
Double voltage = Double amplitude = Logarithmic increase in volume
When you double the voltage of a signal, you double the amplitude of the signal. However, the volume of a signal does not increase proportionally to the amplitude, but logarithmically. Therefore, the loudness of a signal is logarithmically proportional to the amplitude of the signal, but not (directly) to the voltage.
Mixers are a good example for understanding the combination of level and decibels. Basically, a mixer is a voltage distributor and voltage amplifier. Do you need to amplify an audio channel by 6 dB, for example to make the background music louder in a certain area? Then move the slide control of the mixer up and double the voltage (for example). This will result in an increase of 6 dB. This means that the level is 6 dB higher compared to before because we doubled the voltage.
In plain language this means that voltage and sound wave amplitude are indirectly related because sound waves are transmitted using electrical signals. For example, sound waves are generated in loudspeakers using electrical signals that are passed through a loudspeaker core. The voltage of the electrical signal determines how fast the speaker core is moving and thus provides the amplitude of the sound wave produced by the speaker. In this case, the voltage of the electrical signal has an indirect effect on the sound wave amplitude, as it affects the movement of the speaker core.
As far as sound pressure levels, voltage and decibels are concerned, the core usually deals with (sound wave) amplitudes.
The amplitude of a sound wave …
is the difference between the maximum and minimum pressure exerted by the wave or signal. The greater the amplitude of a sound wave or acoustic signal, the louder it is perceived.
is measured in pascals (Pa) and indicates the pressure difference caused by the sound wave. Sound pressure is the pressure a sound wave exerts on the environment.
is often used as a reference value to describe the volume of sound waves or acoustic signals. The amplitude of a sound wave depends on many factors, such as the type of sound source, the frequency of the sound wave, and the characteristics of the transmission channel. For example, lower frequencies will usually be of greater amplitude than higher frequencies because they carry more energy. The amplitude of a sound wave can also be affected by the properties of the transmission channel, such as the attenuation or absorption of sound energy by materials or the reflection of sound energy from surfaces.
|Voltage / Amplitude x10||Increase by 10 dB|
|Voltage / Amplitude x100||Increase by 20 dB|
|Voltage / Amplitude x1000||Increase by 30 dB|
However: We can never tell how much louder +20 dB really is without knowing how strong the sound pressure was beforehand. This is because an increase of 6 dB turns differs depending on how high the sound pressure was before.
When cross-checking the relationship between decibels and voltage, this means: If we lower the volume by 6 dB starting from 0 dB, we lower the voltage via our slide control on the mixer or amplifier. The output level is now -6 dB (less than before). This evidently explains how negative decibel values can be achieved.
Another example: Decibels for microphones and mixers
Let's say we have a microphone. The microphone emits 10 millivolts of voltage when we speak into it. We connect this microphone to the microphone input on a mixer. Our exemplary mixer (or more precisely: the preamplifier of the mixer) has an amplification of 40 dB. The table above suggests that 40 dB corresponds to a linear ratio of 100. Therefore, a preamplifier with an amplification of 40 dB will amplify our 1 mV microphone level signal by a factor of 100. So, we receive 1,000 mV or 1 V. Consequently, the level of the pure, unaltered microphone signal is initially -40 dB compared to the amplified line level of the mixer. This means that the incoming power of the microphone is 1/100 of the output of the preamplifier and thus of the mixer. This is also a realistic widespread standard. A good microphone preamplifier should increase the signal by at least 40 dB (x 100). An amplification of up to 60 dB (x 1000) is usually not required, but many microphone amplifiers can also do this. Most mixers have a slide control at the top of each channel to control the amplification. This allows you to adapt the mixer to the input level of the microphone.
So find out what level your microphone input on the mixer “expects” from the microphone (or another source). If you feed in more, this will likely lead to distortions.
dBV, dBu, dBm? The decibel scale with other units of measurement for power
Feel like you are stumbling through all the variations of the decibel scale?
0 dBV means that 0 dB is one Volt (1 V).
0 dBu means that 0 dB corresponds to 0.775 Volts. It's a voltage level that emits exactly 1 mW of effective power output at 600 ohms.
0 dBm means that 0 dB is also 0.775 Volts, but the power formula must be used for decibel calculations, i.e. 1 dBm is equivalent to 2 dBu.
A line level of -10 dBV corresponds to a voltage of 0.3162 Volts. This line level is sometimes used as a reference level, but there is no common line level in entertainment electronics. The choice of line level depends on the specific needs of the user. The term “line level” is typically used in reference to the electrical line/wire used to transmit an audio signal from one device to another. Line level indicates how loud the audio signal is at the input of a device. Generally, the line level is specified in Volts.
When measuring power (that is, in watts), decibels are calculated as follows:
dB = 10 x log10 (L1/L2). That means: L1 is the output power, L2 is the reference or input power. If we apply a power level (L2) of 1 watt and the measured power level (L1) at the other end of the cable is 0.5 watts, 50% of the signal has been lost through attenuation. If you enter these values into the formula, you get a value of 3 dB. So that means:
Every 3 dB of attenuation results in a loss of 50% of the signal power over the cable. A low attenuation value is desirable since that means that a higher power level will arrive at the destination.
- Every 3 dB of return attenuation means 50% less signal power is returned to the source. A high decibel value for the return attenuation is desirable. This means that less power is fed back to the source.
- Every 3 dB of NEXT (a measurement of the suppression of crosstalk between two adjacent pairs of wires in a line) means that 50% less signal power can be coupled into adjacent pairs. High decibel values for crosstalk values are good since that means that less power is coupled into adjacent pairs.
Power ratings and cable testers typically refer to voltage ratios rather than power. In that case, we need to calculate the decibels a bit differently. This is how we do it: dB = 20 x log10 (P1/P2). P1 stands for the input voltage or input current and P2 for the reference voltage or reference current (or the output current). If we use a reference value of 1.0 Volt for P2 and 0.5 Volts for P1 (the measured input), we receive a value of -6 dB. That in turn means this:
- Every 6 dB of attenuation means that 50% of the voltage is lost through attenuation. Lower decibel attenuation values are desirable here as well, since a higher voltage level then arrives at the destination.
- Every 6 dB of return attenuation means 50% less voltage is returned to the source. Higher decibel values for the return attenuation are desirable here as well, since less voltage is fed back to the source then.
Accurately interpreting decibel readings is difficult due to environmental factors that affect measured values or confusion of relative values within different scales. Despite these challenges, the decibel scale is increasingly being used in sectors ranging from underwater navigation to virtual reality headsets and beyond. Are you interested in learning more about PA Technology, PA applications and DIY projects? Check out our Magazine.
Headergraphik: Adobe Stock / mpix-foto