Decibel

History of the bels and decibels

The Bel (symbol B ) is used in the Télécommunications, the electronic , and the Acoustique. Invented by engineers of the Laboratories Beautiful to measure the attenuation of the audio signal on a distance from a mile (1.6 km), standard length of a cable of Telephone, it was called unit of “transmission” in the beginning, or YOU (in English), but was famous in 1923 or 1924 in the honor of the founder of the laboratory and pioneer of the télécoms, Alexander Graham Bell.

Definition

The decimal logarithm of a report/ratio of powers:

\ log_ {10} \ left ({P_1 \ over P_ \ circ} \ right)

express yourself into Beautiful. Such a measurement multiplied by ten:

10 \ log_ {10} \ left ({P_1 \ over P_ \ circ} \ right)

is thus expressed in decibel (dB). A decibel being equal to a tenth of Beautiful.

For example, if the relationship between the two powers is of: 10 = 100, that corresponds to 2 Bel or 20 dB.

In certain situations the powers are proportional to the square of another size. For example in electronics if one works with constant resistances of load, or in acoustics, the sound power is proportional to the square of the acoustic pressure. Often, in these situations, if one expresses the power according to the other size, of the squares appear, and it is trying for the mathematicians to leave them the logarithm to arrive at definitions of decibel of the kind:

dB = 20 \ log_ {10} \ left ({U_1 \ over U_ \ circ} \ right)

But it is to better retain the definition of origin.

The decibel like absolute measuring unit

The decibel is used like measures relationship between two powers in certain fields, like the Télécommunications or the Radar to describe profits or amplifications (dB positive) or losses or attenuations (dB negative). One speaks then about an attenuation of 15 dB compensated by an amplifier with 15 dB of profit. An attenuation of 15 dB is equivalent to a profit of -15 dB.

The decibel gave rise to a certain number of units (without dimensions) used to measure powers or intensities absolutely. This is done by using as power of reference (in the denominator of the preceding definition) a value of preset power. In this case, one adds a letter to “dB” to know of what one speaks. Here some examples:

dBSPL decibel in acoustics (see low);
dBa decibel balanced in acoustics (see low);
dBW decibels with the top of one Watt. The power of reference is 1 W;
dBm decibels with the top of one milliwatt. The power of reference is 1 MW;
dBu decibels measuring the tension compared to a reference of 0,775 Volts RMS. This value of reference corresponds to the tension of a load of 600 Ohms subjected to 1mW.
dBV decibels measuring the tension compared to a reference of 1 Volt RMS.
dBi used to speak about the profit of the antennas. The profit of reference is that of an antenna Isotrope.
dBFs: amplitude of a signal compared to its maximum level before saturation.

Acoustic unit

dBSPL

Decibel, noted dB, is a relative unit of the acoustic intensity. The dBSPL ( Sound Presses Level ) is defined by the report/ratio of the power per unit of area of the sound which one measures and a power per unit of area of reference:

dB_ \ mathrm {SPL} = 10 \ log_ {10} {\ left ({{P \ over S} \ over \ left ({P \ over S} \ right) _ \ mathrm {R \ acute {E} F}} \ right)} \

The power per unit of area of reference is 10^-12 W· m^-2 (a picowatt per square meter).

The power per unit of area transported by a sound wave is connected to the acoustic pressure by the formula:

${P \ over S} = {1 \ over \ rho v} p^2$

where:

$\ frac {P} {S}$ is the power per unit of area (in W· m^-2).
$p$ is the effective acoustic pressure (in Pascal).
$\ rho$ is the density of the medium (in kg· m^-3).
$v$ is the speed of sound in the medium (in m· s^-1).

If, in the formula of the first definition, one replaces the power per unit of area by the formula according to the acoustic pressure, the density and speed are simplified and one obtains:

dB_ \ mathrm {SPL} = 10 \ log_ {10} \ bigg (\ frac {p^2} {p_0^2} \ bigg) \

If one leaves the square the logarithm one the second version of the definition of dBSPL obtains:

$dB_ \ mathrm {SPL} = 20 \ log_ {10} \ bigg (\ frac {p} {p_0} \ bigg) \$

$p$ is the pressure level of the sound (in effective value) and $\ textstyle {p_ \ circ}$ is the pressure of reference which one accepts as the level from which the human ear starts to perceive a pure sound of 1 Khz. This one is of 20 µPa (effective value). Two values of reference (1 picowatt per square meter and 20 µPa effective) is equivalent for the air to the temperature and environmental pressure.

In addition, for the same acoustic level at various frequencies, the man does not perceive the same level of intensity. For the same level of acoustic intensity of 20 dBSPL, a pure sound of 1 Khz will appear stronger than a sound of 10 Khz while a sound of 100 Hz will not be perceived. To have the same perceived level, the sound of 10 Khz will have to be with 30 dBSPL and the sound of 100 Hz with 50 dBSPL. The isosonic Courbes represent the of the same curves perceived intensity as a pure sound of 1 Khz on a given acoustic level.

The auditive threshold of feeling

The level of 0 Phon or 0 dB SPL is a really low level. To realize it, here to what this level of 0 dB SPL corresponds:

in power per square meter: with 0,5 Watts left again on all the surface of the Metropolitan France;
in pressure: with the pressure due to the weight of a layer of 2.10 -9 m of water (approximately 20 atoms thickness);
in displacement of the molecules in the air: with an oscillation (peak with peak) of 2.10 -11 m, i.e. 2 tenth thickness of an atom!

balanced dB

To take into account this sensitivity of the ear compared to the frequencies, the dB (A) is used. Indeed, this one uses the isosonic curve, corresponding to a perceived level of 40 dB for a pure sound of 1 Khz. The reverse of this curve balances the signal and one obtains the level in dB (A) by integration on all the frequencies. This unit is very frequently used in the acoustic indicators of the noise.

Various examples on the scale of the noise

From 0 to 10 dB: desert
From 10 to 20 dB: cabin of sound recording
From 20 to 30 dB: conversation with low voices
From 30 to 40 dB: forest
From 40 to 50 dB: library
From 50 to 60 dB: dishwashers
From 60 to 70 dB: television set
From 70 to 80 dB: vacuum cleaner
From 80 to 90 dB: lawn mower
From 90 to 100 dB: road with dense circulation
From 100 to 110 dB: power pick
From 110 to 120 dB: discotheque
From 120 to 130 dB: plane on takeoff (with 300 meters)
180 dB: takeoff of the rocket ARIANE

Below 20 dB, the sound are practically inaudible for the human ear. It starts to become painful beyond 80 dB, dangerous from 100 dB and straightforwardly unbearable as of 120 dB.

See too

Sonometer

External bonds

Converter: http://www.temcom.com/pages/dBCalc_fr.html

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