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How do decibels work?

Loudest Recorded Sounds on the Planet
December 16, 2019

How do decibels work?

How do Decibels work?

Decibels are used to measure and describe the waves of sound in air.

First let us define sound.
Sound itself is a wave, or an alteration in pressure, particle displacement or particle velocity propagated in an elastic material or the superposition of such propagated alterations. Sound is also the sensation produced through the ear as we perceive them. Sound is produced when air is set into vibration by any means whatsoever, but sound is usually produced by some vibrating object which is in contact with the air. If a string, such as the one used in a banjo or guitar is plucked, sound produced which dies down in a fairly short time. When the string is plucked it tends to spring back into its rest position, but due to its weight (mass) and speed (velocity) it goes beyond its normal position of rest. Then, in returning it again goes beyond its normal position of rest. The excursions become smaller and smaller and finally the string comes to rest. As the string moves forward it pushes air before it and compresses it, while air rushes to fill the space left behind the moving string. In this way air is set in motion. Since air is an elastic medium, the disturbed portion transmits its motion to the surrounding air so that the disturbance is propagated in all directions from the source of disturbance. The way we measure this sound, or disturbance, is through the use of the decibel.
A decibel is the standard unit of measure, in acoustics, for level difference. The decibel scale is based on the ratio 10^(1/10); multiplying a power-like quantity (such as sound power, or mean square sound pressure) by this factor increases its level by 1 decibel. If a power-like quantity if increased by a factor of 10^(n/10), its level goes up by n decibels. The unit symbol for which is dB. Here the university of Indiana goes into depth on the bel and decibel.

Note: Separate units are commonly adopted in acoustics and signal processing for levels, which relate to power-like quantities and are measured in bels or decibels, and logarithmic magnitude ratios, which relate to harmonically-varying quantities and are measured in nepers.
The range of sound pressure magnitude and sound power experienced in practice is very large. Thus, logarithmic rather than linear measures are often used for sound pressure and power. The most common is the decibel. The decibel represents a relative measurement or ratio. Each quantity in decibels is expressed in a ratio relative to a reference sound pressure, power, or intensity. Whenever a quantity is expressed in decibels, the result is known as a level.
The decibel (dB) is the ratio R1 given by the following formula below:
Thus, R1 = 10^(0.1) = 1.26. The decibel is seen to represent the ratio 1.26. A larger ratio, the bel is sometimes used. The bel is the ratio R2 given by Log(R2=1).
Thus, R2 = 10^(1) = 10. The bel represents the ratio 10. The sound pressure level Lp is given by the following formula below:

The table below shows some typical sound pressure levels for reference:
The table below shows some typical sound power levels for reference:

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