What is decibel (dB)?

What is a decibel?

To understand the dB, we need to learn Exponents and Logarithm first,

What is Logarithm and how it is related to the exponents?

Here's a simple example:

100=102=10×10$$$$

Here, the little 2 is called the exponent. It means multiply 10 by itself twice. Similarly, for:

1000=
103=10×10×10$$$$

3 is the exponent, and means multiply 10 by itself 3 times.

A logarithm is the exact opposite of an exponent. Take another simple example. This is pronounced "the logarithm to base ten of one thousand equals three":

log101000=3$$$$

10 is called the base. The logarithm of 1000 is simply the number of times the base (in this case 10) must be multiplied by itself to get to 1000, i.e. 3 times. And you should notice that this is just the same as the exponent from the equation above. Each equation uses the same three numbers, just arranged in a slightly different way.
Now, the strange thing is that exponents and bases don't have to be whole numbers. In fact, they can be any numbers at all. Here is a completely random example:

64.7=4542.6674

log64542.6674=4.7$$$$

One important rule to learn is that the logarithm of 1 is always zero, regardless of its base.

The decibel

The decibel (dB) is one tenth of a bel and is named in honour of Alexander Graham Bell. The intensity in dB of a sound of intensity I is given by

I(dB)=10log10[II0]

It is a relative unit which means it only makes sense when you have a reference level to compare to. For our reference we use the threshold of human hearing. The quietest thing any human can hear, I0, is one trillionth of a watt per square meter. So, if a sound is twice as intense as I0, its intensity will be

10log10[2I0I0]=10log102=3dB

Scenario	Number of times more intense than I0	Intensity in dB
Limit of human hearing	1	0
Sound of Breathing	10	10
Whispering	100	20
Loud Conversation	100,000	50
Busy Street	10,000,000	70
Thunder	10,000,000,000	100
Jet Plane on Take-off	100,000,000,000,000	140
Space Rocket Launch	10,000,000,000,000,000,000	190