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When we hear a light music we are very comfortable but a loud noise like a drum beat the comfort level comes down. It becomes worse when a bomb is exploded. This is because of the increase in ‘Loudness’ of the sound. The loudness of a sound is a measure of its intensity. The unit which is commonly used for measuring sound intensity is decibel. In this article we will study how this unit has been defined and is in vogue.


Decibel Definition

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The practical unit of measuring the intensity of power is ‘Decibel’ and generally denoted in abbreviation as ‘db’. Though it applies to intensities of different types of powers, the unit is more prominent in acoustics. The unit ‘bel’ is equivalent to 10 decibels but this unit is not common in use. Decibel is an empirical unit of comparing the intensity of power given out by an object to particular reference power intensity. Because of large variations of the ratios in powers, the logarithm of the ratio of the given intensity to a particular reference intensity is considered as the scale.
Let P is the intensity of power given out by an object during its function and Po be a reference power intensity. The decibel formula or the decibel scale is derived as,

$I_{db}$= $10\log \frac{P}{P_{0}}$,

where Idb is the intensity in decibels. This is the basic definition of a ‘decibel’.

Decibel Examples

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Let us describe the decibel measures related to sound. As mentioned earlier we are comfortable to hear a light music which has a measure of about 70 db. But a noise from a drum beat can be around 80 db. It actually means that the noise of the drum beat is about 100 times more intense (louder). In other words, for every increase of 10 decibels (a bel), the variation in intensity is 10 times the original intensity.

Decibel Conversion

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The reference power intensity in acoustics is the intensity of sound when absolute silence is maintained. Thus when there is a silence, the ratio is 1 and hence the decibel level of silence is 0. Suppose P is the intensity of a sound source, then decibel conversion for that intensity is given by,
$I_{db}$= $10\log P$

Decibel Formula

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In general cases, the unit ‘bel’ is defined as the logarithmic ratio of two power intensities; one is known power intensity and used as reference. Suppose P is the intensity of a sound source and Po is the measure of known intensity,

then $I$(in bels) = $\log$$\frac{P}{P_{0}}$ and hence the decibel formula is,
$I_{db}$= $10\log$$\frac{P}{P_{0}}$

The decibel formula is generally used to determine the decibel level of a power intensity. However, sometimes, we know the decibel level of some power generations from other knowledgeable sources. We might be interested to know the impact of that power source. In such cases, the decibel formula is modified as decibel equation as shown below.

$\frac{P}{P_{0}}$ = $10^{(\frac{I_{db}}{10})}$ 

$P$ = $P_{0}\times 10^{(\frac{I_{db}}{10})}$

Decibel Measurement

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Decibel levels of various power generations are measured in different ways. Main principle in decibel measurement is based on audio electronics. That is the principle of conversion of sound energy to electrical energy. The basic principle is similar to a telephone circuit. It receives the sound and converts it to electrical pulses. With necessary integration circuits, the sound level is calibrated in decibels.
A decibel meter, as the name suggests, is an instrument for measuring the sound level. It is abbreviated as ‘dB meter’ and also called as ‘Sound Level Meter’. The undesirable noise levels are termed as ‘noise pollution’ in human society. Hence strict impositions are effected on noise levels in places like hospitals, road traffics, churches and other worshiping places, meditation halls etc.

To monitor the noise levels in such places decibel meters are installed and with suitable feed back systems, violation of noise control limits can instantly be detected. Further with the help of decibel meters on can take necessary hearing protections for those who need to work in noisy situations.
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Decibel Chart

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To perceive the Unit of Decibel, Decibel Chart in various real life situations is shown below.

Human breath 10 db
Whispering 20 db
Quite locations 30 db
Noise in a quite library40 db
Normal conversation( homes)50 db
Normal conversation (offices)60 db
Light music
70 db
General noise in factories 80 db
120 db
Jet plane take off 150 db

Continuous exposure to sound of decibel level of 90 – 95 db might damage human ear tissues. A sound intensity of 140 db, even for a short exposure is dangerous to human ears and might lead to deafness. People who work in such environments are advised to use hearing protections. A loudness of 180 db can instantly kill the hearing tissues.
In cases of earthquakes, the intensity is expressed in numbers, followed by the term ‘Richter’s Scale’, as a common and convenient unit. For example an earthquake measured as 5 in Richter’s scale is 10 times more intensive than that of an earthquake measured as 4 in the same scale. Similarly in acoustics the intensities are measured in decibels as explained in all the sections. These decibel nomenclature is also called Decibel Scale in Acoustics.
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More topics in Decibel
Decibel Meter Decibel Scale
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