What is decibel [dB]? How to calculate and add decibels

　・In Japanese
Premise knowledge
　・Logarithm

■What is decibel [dB]?

Decibel is a unit of sound loudness. The volume of sound is originally measured in sound pressure (unit: Pa), but sound pressure has a wide range of values, and as the value increases, the loudness perceived by humans becomes less consistent with our senses. Therefore, we use logarithms to express the loudness of sound.

＜Derivation of the formula＞
The amount of sound energy passing through a unit area in unit time and the sound loudness level are defined as follows.



Note that decibels are used not only as an index of noise, but also as an index of power and gain in control engineering.

■Characteristics of decibels

When the sound pressure is 20 μPa, which is said to be the limit of human hearing, it is 0 decibels. Also, since the sound pressure increases by 20 dB every 10 times, this characteristic is also called 20 dB/dec. (dec stands for decade)



Explain why logarithms are similar to human sensations. First, graph the relationship between X and dB in the table above. Here, X is the size of the stimulus, and dB is the strength felt by humans.



This characteristic corresponds to the human characteristic that people are sensitive to small stimuli, but feel less sensitive to large stimuli, even though the stimulus increases. This is called Fechner's law, which states that human sensation is proportional to the logarithm of the magnitude of the stimulus.

For example, when changing from 20 dB to 60 dB, the stimulus increases by 100 times while the decibel increases by 3 times, but a 3 times increase is a simple human sensation.

■Addition of decibels

Decibels are logarithmic, so they cannot be added directly. Therefore, 50dB+50dB=100dB will not occur. To add decibels, you need to do the following



From the above, 50dB+50dB=53dB. Also, 50dB+30dB≒50dB, which means that loud sounds are dominant, and quiet sounds have almost no effect on the loudness. You can easily calculate the decibel addition using the table below. The following correction values are added to the larger decibel value according to the difference between it and the smaller decibel value. For 50dB+50dB, the decibel difference is 0, so 50+3=53dB, and for 50dB+30dB, the decibel difference is 10, so 50+0=50.



You can calculate in the same way when adding multiple decibels.



In the case of simple calculations, you can also add the numbers one by one. For example, 50dB+50dB+50dB becomes 50dB+50dB=53dB and 53dB+50dB=55dB.

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