# Decibel

decibel . Unit used for the comparison of power or voltage levels in acoustics and electronics .

The sensation of the ears due to sound waves is approximately proportional to the logarithm of the energy of the sound wave and is not proportional to the magnitude of said energy. For this reason, a logarithmic unit is used to approximate the response of the ear.

Summary

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• 1 Etymology
• 2 Application
• 1 Telecommunication
• 3 Tipo
• 1 Weighted decibel
• 4 Records
• 5 Sources

Etymology

The decibel, whose symbol is dB , is a logarithmic unit . It is a submultiple of the bel , a decibel is the tenth part of a bel, symbol B , which is the logarithm of the ratio between the magnitude of interest and that of reference, but it is not used because it is too large in practice, and that is why the decibel is used.

One bel is equal to 10 decibels and represents a 10-fold increase in power over the reference magnitude. Zero bels is the value of the reference magnitude. Thus, two bels represents a hundredfold increase in power, 3 bels equals a thousandfold increase, and so on.

App

The decibel is the unit of measurement used for the power level and intensity level of noise.

A logarithmic scale is used because the sensitivity of the human ear to variations in sound intensity follows an approximately logarithmic scale, not a linear one. For this reason, the bel (B) and its submultiple, the decibel (dB), are adequate to assess the perception of sounds by a listener. It is defined as the comparison or relationship between two sounds because in studies of physiological acoustics it was found that a listener, made to listen to a single sound, cannot give a reliable indication of its intensity, whereas, if made listening to two different sounds, is able to distinguish the difference in intensity.

As the decibel is a relative unit, for acoustic applications, a hearing threshold of 0 dB has been taken as a convention, equivalent to a sound with a pressure of 20 micropascals , something like an increase in normal atmospheric pressure of 1/ 5,000,000,000. Even so, the true threshold of hearing varies between different people and within the same person, for different frequencies . The threshold of pain for humans is considered to be from 140 dB. This is usually approximately the maximum measurement considered in acoustic applications.

To calculate the sensation received by a listener, based on the measurable physical units of a sound source, the power level is defined, ${L_W}$, in decibels, and for this the power of the sound source to be studied with the power of another source whose sound is at the threshold of hearing , by the following formula:

{L_W}= 10\times \log_{10} \frac{W_1}{W_0(10^{-12})}(dB)

Where W_{1} is the power to study, in watts (variable), W_{0} is the reference value, equal to 10^{-12} watts and \log_{10} is the base 10 logarithm of the relationship between these two powers. This reference value approximates the hearing threshold in air. Note that if W_ is greater than the reference power W_{0} of an ideal isotropic antenna, the value in decibels is positive. And if W_{1} is less than the reference W_{0} the result is negative. Also note that a 10-fold increase in power W 1 relative to the reference means an increase of 10 dB. And that doubling the power W_{1} with respect to W_{0} means an increase of 3 dB.

Sound waves  produce an increase in pressure in the air, so another way to physically measure sound is in units of pressure ( pascals ). And the Pressure Level can be defined , $L_{P}$, which is also measured in decibels.

{L_P}= 20\times \log_{10} \frac{P_1}{P_0}(dB)

Where P_{1} is the sound pressure to be studied, and P_{0} is the reference value, which for sound in air is equal to 2\times 10^{-5} Pa. This reference value is approaches the threshold of hearing in air.

telecommunications

The decibel is perhaps the most widely used unit in the field of Telecommunications due to the simplification that its logarithmic nature makes possible when making calculations with very small signal power values.

As a power ratio that it is, the figure in decibels never indicates the absolute value of the two compared powers, but rather the ratio between them. Unlike what happens in sound, where it always refers to the same reference level, in telecommunication, the reference level is changing.

This allows, for example, the gain of an amplifier or the loss of an attenuator to be expressed in decibels without the need to refer to the input power that is being applied to them at any given time.

The loss or gain of a device, expressed in decibels, is given by the formula:

{dB}= 10\times \log_{10} \frac{P_S}{P_E}

where E is the power of the signal at the input of the device, and S the power at the output of the device.

If there is signal gain (amplification) the figure in decibels will be positive, while if there is loss (attenuation) it will be negative.

To add noise, or signals in general, it is very important to consider that it is not correct to directly add values ​​of noise sources expressed in decibels. Thus, two noise sources of 21 dB do not give 42 dB but 24 dB.

In this case the formula is used:

dB totales = 10\cdot \log_{10}(10^{\frac{X_1}{10}}+10^{\frac{X_2}{10}}+ … ) ,

where X_n are the noise or signal values, expressed in decibels, to add. This formula can also be expressed with the following notation:

dB totales = 10 \cdot \log_{10} \left( antilog\left( \frac{X_1}{10} \right )+ antilog \left( \frac{X_2}{10} \right )+ … \right).

Type

weighted decibel

The human ear does not perceive the different frequencies in the same way and reaches the maximum of perception in the average ones, hence, in order to bring the unit closer to the auditory reality, the units are weighted (so-called isophonic curves are used for this ).

For this reason, the decibel A (dBA) was defined, a unit of sound level measured with a previous filter that removes part of the low and very high frequencies. In this way, after the measurement, the sound is filtered to preserve only the most harmful frequencies for the ear, which is why the exposure measured in dBA is a good indicator of the hearing and vital risk.

There are also other weighted units, such as dBC, dBD, suitable for measuring the reaction of the ear to different loudness levels.

Records

 Sound intensity level. 180 dB Krakatoa volcano explosion . It is believed to be the largest recorded sound in history. 140 dB Pain threshold 130 dB plane taking off 120 dB airplane engine running 110 dB Concert / civic event 100 dB electric drilling machine 90 dB Traffic / Fight of two people 80 dB Train 70 dB Vacuum cleaner 50/60 dB Agglomeration of people 40 dB Conversation 20 dB Library 10 dB calm breathing 0 dB hearing threshold

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