# How does 0 decibels sound

## Acoustics

The essentials in brief...

The hearing can process a huge sound pressure range; however, this does not correspond directly to the volume impression. The hearing has a variable sensitivity.

The logarithmic decibel scale shows the entire volume range from 0 dB (hearing threshold) to approx. 130 dB (pain threshold) in manageable steps.
Sound pressure level resp. Sound level

When calculating with sound levels, it must be taken into account that the sound intensities have to be offset against each other and not the decibel values. A doubling of the sound power corresponds to a sound level increase of 3 dB.
Calculating with sound levels - or when 0 + 0 = 3!

In good conditions, healthy hearing can distinguish levels of 1 dB in a direct comparison.
Differentiation of level differences through our hearing

The hearing is not equally sensitive in all frequency ranges. In general, low tones are perceived as less loud at the same sound level. This is why hearing deviates from the decibel scale.
Volume and loudness: phon and sone

The loudness scale in [sone] is based on the fact that 0.5 sone are half as loud as 1 sone and 9 sone are three times as loud as 3 sone. This subjective scale depicts the hearing sensation in a linear manner.
Loudness scale in sone

Measurement filters are used to correct the deviations of the sound measurements from the auditory impression. Today the A filter is mostly used and the sound levels measured with it are given in dB (A). The measuring filters try to simulate the phon curves.
Deviations of hearing from the decibel scale: The dB (A) rating

"Volume" cannot be measured! What is measured physically is the sound pressure, which is then converted into a sound level and converted into dB or dB (A) is specified.
The measurement of sound

The energy-equivalent continuous sound level Leq is a meaningful variable in sound level measurement. The Leq averages the sound energy over the measurement period and not the sound level.
The energy-equivalent continuous sound level Leq

### Sound pressure

The audible pressure fluctuations are tiny compared to the atmospheric pressure. In physical terms, they are superimposed on the prevailing air pressure and are referred to as sound pressure. The abbreviation for sound pressure is P and the unit is Pascal [Pa].
Our hearing is designed to register the rapid fluctuations in air pressure. During a normal conversation, these rapid air pressure fluctuations are around 0.05 Pa (1 / 2,000,000 of the atmospheric pressure). Weather changes, however, cause the air pressure to fluctuate by several thousand Pa within days! The sensitivity of the hearing is important in order to ignore slow pressure fluctuations, such as those caused by the difference in height when climbing stairs (several tens of Pa) or when the weather changes. The existing static air pressure works equally on the outside and inside of the eardrum. Therefore it has no influence on hearing. The pressure equalization between the outside and inside takes place via the so-called Eustachian tube. When yawning or other jaw movements, this connection between the pharynx and the middle ear is opened and the pressure is equalized.

### Sound pressure level

The hearing can process a huge sound pressure range, namely from 0.00002 Pa (hearing threshold) to approx. 20 Pa (pain threshold). This corresponds to six orders of magnitude! However, such information in no way corresponds to the volume impression. The ear has a variable sensitivity: a large one for weak signals and a small one for strong signals. Since the sound pressure of a tone is so small, the sound pressure of a tone is compared with the pressure of a barely perceptible tone at 1 kHz to indicate the strength of the sound. This relative reference is called the sound pressure level L, or sound level for short. The dimensions are given in decibels [dB]. The introduction of this scale shortens the range of values ​​considerably, the sound pressure values ​​from 0.00002 Pa to 20 Pa are represented by the decibel values ​​from 0 to 120 dB. The decibel scale was defined as a logarithmic scale.

The sound level can be calculated from the sound pressure and the reference sound pressure (hearing threshold at 1 kHz) using the following formula:

[dB]
 p: Effective sound pressure [Pa] p0: Reference sound pressure (p0 = 0.00002 Pa)

Since our hearing works approximately logarithmically, the decibel measure results in a better correspondence with the volume impression of a signal. We always perceive an increase in the level of 10 dB as a doubling of the volume. At best, a person can perceive differences of one decibel.

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### Calculating with sound levels - or when 0 + 0 = 3

Sound level values ​​have the disadvantage that they cannot simply be added. What adds up from two sound sources is namely their sound power (or intensity), which is proportional to the square of the sound pressure. To double the sound power, the sound pressure only needs to be increased by a factor of √2! In principle, it is not the individual sound level values ​​that have to be added, subtracted or multiplied, but the individual sound power levels. The result obtained is then converted into a sound level.

For example, the following applies to the addition of two sound sources with 0 dB each:

0 dB + 0 dB => 3 dB.

The following also applies to two sound sources with 65 dB each:

65 dB + 65 dB => 68 dB.

The following relationships apply:

 Doubling the sound power: + 3 dB (because 20 log (√2) = 3.01) Doubling the sound pressure: + 6 dB (because 20 log (2) = 6.02) Tenfold increase in sound power: + 10 dB (because 20 log (√10) = 10) Tenfold the sound pressure: + 20 dB (because 20 log (10) = 20) (log means the 10th logarithm)

The formulas for sound power are used when there are several sound sources or when the power of a music system is increased. The formulas for the sound pressure are needed if z. B. a loudspeaker membrane is deflected twice as much, i.e. if you double the AC voltage on the loudspeaker.

 Comparison of the three measures of sound power, pressure and level with the different size scales.

The amount of energy transmitted to the ear with the sound is decisive for damage to the ear. Energy is the product of performance times time. The hearing-damaging effect of sound is therefore equal to the product of sound power and exposure time.

If different dB values ​​have to be added, this is calculated as follows:

 [dB]

L.1, L.2 denote the individual sound levels in dB. This formula first converts the sound levels into sound power levels, adds them and then goes back to the dB scale. Other sound pressure levels are analogous to the terms with L.1, L.2 added.

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### Differentiation of level differences through our hearing

 Level differences, 0 to +10 dB. Repeated, electronic organ sound, the level of which has the following values ​​relative to the first level: 0, +1, 0, +3, 0, +6, 0, +10, 0 dB. SuvaPro Audio Demo 3, Track 14

Our hearing quickly adapts to existing sound levels. The differences in levels are most pronounced when we hear two levels immediately after one another. The smallest audible difference depends on the level and frequency. About 1 dB should be audible. Where our hearing is most sensitive, namely at 4 kHz and very high levels from 80 dB, a difference of 0.25 dB is at best noticeable.

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### Volume and loudness: phon and sone

Two tones with the same sound level but different frequencies are often perceived as differently loud. In addition to the physically measurable quantity (sound pressure, sound pressure level), a purely subjective quantity, the volume, was also defined. The volume is given in [phon] and its definition is based on the subjective comparison of two sound processes. For this comparison, the 1 kHz tone was chosen as the reference tone. The volume scale therefore corresponds exactly to the decibel scale at 1 kHz. In order to determine the volume of a certain sound process (signal), one compares the existing signal with the 1000 Hz reference tone. The intensity of the reference tone is now changed until it is perceived as being as loud as the existing signal. The sound level that can be read off the reference tone then corresponds to the volume of the generated sound process in phon.

 Source ISO standard 226 (supplemented) Internationally standardized curves of equal volume for pure tones. The orange line marks the reference frequency of 1000 Hz, where decibels and phons are equal. A 20 Hz tone with 110 dB is perceived as being as loud as a 4 kHz tone with 70 dB, both times it is 80 phons.

The curves of the equally perceived loudness of pure tones were determined on the basis of numerous studies with normal hearing people between the ages of 18 and 25 years.

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### Loudness scale in sone

A change of 10 phons is subjectively as a doubling or. Perceived a halving of the volume. In order to better grasp this fact, a further, subjective measure was introduced: the loudness, measured in [sone]. The loudness scale is based on the fact that 2 sone are twice as loud as 1 sone and, analogously, 0.5 sone are half as loud. The reference value is 40 phons, where 1 sone is defined. The conversion from phon to sone works as follows:

 [sone] The following loudness diagram is calculated from this: Loudness diagram. The reference value 1 sone is 40 phons. 10 sone are ten times as loud as 1 sone, 0.5 sone are half as loud as 1 sone. Note the logarithmic scale of the y-axis.

The great advantage of the loudness scale in sone lies in the directly readable comparability of loudness information. The disadvantage is, as is the case with phon information, that the values ​​are subjective and cannot be easily recorded with any measuring instrument. Volume specifications in phon or sone were still widespread in the 1970s, but were then increasingly replaced by the so-called dB (A) values. In the meantime, loudness information is increasingly being given in sone in the field of air conditioning and ventilation technology and also for PC hardware. Although this information is very useful for comparisons, the sone values ​​are usually not measured directly, but are calculated from dB (A) measurements and the frequency band. No wonder, since a sone measurement would also require the sensitive ears of a large number of test persons in order to achieve a statistically useful result.

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### Deviation of hearing from the decibel scale: The dB (A) rating

Various filters have been developed to adapt the measurements of sound to our hearing. These filters correct the measured values ​​in a certain frequency range in order to better suit the sensitivity of the ear. The A filter, for example, attenuates the bass and treble. As a result, an A-weighted measurement result looks similar to a phon curve. Other filters were labeled B, C, and D. All of these filters have been optimized for a certain range of the decibel scale, the A filter for low sound levels, the D filter for very high levels.

By using such a filter, the stated measured value is more in line with our perceptions and can be measured relatively easily. In order to increase handling and comparability, the A filter is almost exclusively used today for measurements, regardless of whether the sound processes involved are loud or quiet. The A-weighting of the sound level is given in dB (A), but can otherwise be handled and added up like dB values.

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### theory

As the name suggests, the sound (pressure) level is measured with the sound level meter. Mostly the information is given in dB (A).

 Various handy sound level meters. Source: SUVA

But the question is what is actually being measured, or how long should it be measured? Different types of sound events occur on a street. When a car drives by, the noise level is higher than when nothing is passing by. Nevertheless, it is usually not absolutely quiet even then. These fluctuations can be captured in a number of ways. You can measure the maximum level while the vehicle is passing through, but it is also possible to measure the average value over several minutes. But what is most interested in is the average sound level at the measurement location, which is required for assessing the noise situation. For this purpose, the impulsiveness and the information content of a sound source must also be taken into account.

### Device types

There are different types of devices for measuring the sound level. On the one hand the typical ones Sound level meter:

• The standard devices average exponentially and virtually show a snapshot of the sound level. The sound is converted into an alternating current signal in the microphone and then converted into a direct current signal by means of quadratic averaging. The time segments to be used for averaging are internationally standardized to ensure comparability: 'S' uses an interval of 1 s, 'F' one of 125 ms. The result can be corrected using a filter (see db (A) evaluation) and is logarithmized so that the result can be output as dB.

 Scheme of sound level measurement. The sound is converted into electrical current, which is specifically changed in various circuits and at the end the result can be read on a display (analog or digital).
• Integrating averaging devices are better for determining noise exposure, in this case the sound is integrated ('summed up') after filtering. The result is Pa2 · s in SI units, but the SEL level associated with the Leq can also be displayed instead. Some devices allow an immediate octave band analysis, which makes it possible not only to determine the overall sound level, but also the individual components of the various frequency ranges.

A slightly different, specialized type of device for measuring sound includes the Ear simulators. They are mainly used for testing and measuring headphones and hearing aids, but also for calibrating audiometers that are used to determine hearing ability. The complexity of such devices varies greatly, from simple hollow cylinder-like shapes to constructions that try to mimic the properties of the human ear with the help of a suitable shape.

Noise dosimeter are closely related to the radiation dosimeters that are used, for example, by workers in nuclear power plants: they are worn on the body and say something about how much noise a person has been exposed to over a long period of time. The sound level is continuously measured and virtually added up; the result is usually in the unit Pa2 · h. Modern noise dosimeters are very small and can be carried on the shoulder, for example. Since they do not require cables or the like, the integrity of the device is always guaranteed.

 A noise dosimeter ('doseBadge') from Pulsar Instruments Plc. Source: Pulsar Instruments Plc

### accuracy

In terms of application, there is a need for a measurement resolution that is an order of magnitude better than that of the limit values ​​of interest, i.e. 0.1 dB. This results in a required accuracy of ± 0.05 dB. In relation to the hearing ability of the human ear, an accuracy of 1 dB would in principle be sufficient.

There are two important values ​​in determining the accuracy of sound level meters:

• (Amplitude) frequency response: Deviation from the measured to the true sound level depending on the frequency. The values ​​in the frequency range from 20 Hz to 20 kHz are important.

• Dynamics: Deviation from the measured to the true sound level at a certain frequency depending on the volume. The dynamics are only good in a certain interval (usually 100 - 120 dB). The lower limit of this range is where the signal noise, which is always present for technical reasons, drowns out the useful signal, and its upper limit is where overloading of the recording device leads to signal distortion (overdrive, also known from the hi-fi sector).

The measuring devices themselves are divided into two classes, which are regulated in the standard of the 'International Electrotechnical Comission' IEC 61672. Class 1, which is used in the laboratory and in the field, must be able to measure a wider frequency spectrum more precisely than class 2, which is mainly used for less specialized matters in the field, i.e. the requirements are higher.

### The measurement

With regard to the measurement process itself, three things are essential:

• The measuring device requires a correct and regularly repeated calibration. This must be traceable to a primary standard in an uninterrupted chain.

• The measurement method itself must be standardized, ideally internationally by a corresponding standardization organization.

• The person performing the measurement must be informed about the correct procedure and, depending on the complexity of the device, trained to use it.

Only under these conditions is a correct and above all comparable result guaranteed, which could also serve as the basis for a court decision, for example.

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### The energy-equivalent continuous sound level Leq

Thanks to the use of electronics, it is now possible to use relatively simple measuring instruments to measure a quantity that is far more meaningful than the pure average value of the level. This quantity is called the energy-equivalent continuous sound level Leq, also called the averaging level or intensity mean. Energy equivalent means "containing the same energy", "corresponding to the same energy". In principle, the sound energy of the (constant) Leq level corresponds exactly to the average sound energy of the fluctuating sound event. The device measures the sound level over a period of time, calculates the energy of the sound from this and adds up these energy values. At the end of the time span, the total energy is averaged over the time span and output as Leq in dB. Formally this means:

 [dB resp. dB (A)]
 Leq: Average level [dB, dB (A)] T: Measurement duration (= sum of all ti) [s] ti: Duration of the level value L.i [s] L.i: Level during the period ti [dB, dB (A)]

Source: Werner Stalder, (2000). "Education and training course on noise protection", p. 2.8

Graphical representation of a sound level measurement. Both the average sound level L and the energy-equivalent sound level Leq are shown. Because the energy content of high sound pressures is much greater than that of small ones, the Leq value is much higher than the mean sound level L.

The main advantage of the energy-equivalent continuous sound level is that it can be used to characterize a sound event that fluctuates over time with a single assessment variable

The Leq is useful as an assessment parameter for a wide variety of types of noise. In the case of industrial or commercial noise with significant impulsiveness of the sound events, the Leq can be problematic because the disturbing peak values ​​can then be "diluted". Nevertheless, the Leq is also used for such types of noise. The subjective disturbance caused by the impulses is compensated afterwards with a level correction.

### The SEL level

In noise abatement practice, the so-called SEL level (sound exposure level) is often determined in addition to the Leq. The sound energy of the SEL level corresponds exactly to the sound energy of the Leq level; however, the averaging is not taken over the assessment period, but over an exposure time of 1 second. For example, the energy sum from 3 minutes of measurement time is concentrated in one second, i.e. the SEL value is generally greater than the Leq.

The SEL is calculated from the Leq as follows:

 [dB resp. dB (A)]

With the SEL level, the energies of sound events can be compared, which have different duration and intensity.

In addition to these variables, there are a number of other key figures, especially for long-term measurements over days and nights, where certain daytime corrections are necessary to assess the noise nuisance.

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