Decibel (dB) - definition and formula

Definition of the Concept

Almost everyone has heard of the decibel at least once in their lifetime, but what is it really? Let's try to explain this. 

The decibel is primarily a logarithmic and dimensionless unit. This simply means that it defines a measure of ratio quantities and requires some reference, as it is not an absolute scale unit in itself – like a meter, for example. Everyone knows what a meter is.

In the case of broadly understood acoustics, you can very often encounter the decibel indicating the level of sound pressure, known as dB SPL (sound pressure level). However, it should be mentioned that there are many different “types” of decibels – each with its own unique purpose in physics.

Formula (dB SPL)

The decibel (dB SPL) we mentioned is given by the following formula:

where:

• p – measured sound pressure in Pa

• p0 – reference sound pressure in Pa (equals 20 μPa)

The value 20 μPa is not unreasonably the most common reference pressure. It is nothing more than the minimum value of sound pressure that a human can “detect” by the hearing organ at a sound frequency of 1000 Hz. This is the threshold of hearing. The frequency was chosen for a reason, as it is a value in the range where the human ear is most sensitive.

This formula leads to the conclusion that a level of 0 dB SPL is the sound pressure equal to the reference sound pressure, meaning the threshold of hearing. Simple? Quite so. 

Decibel as a Logarithmic Value

Since the decibel is not a linear measure, but logarithmic, it is worth noting that doubling the value of the measured sound pressure does not lead to doubling the decibel value. This naturally results from the previously given formula. A simple example – let's take a pressure p1 = 200 μPa and p2 = 400 μPa. After substituting into the formula, in the first case, the dB SPL level will be 20 dB SPL, while in the second about 26 dB SPL. Thus, for doubling the value of the measured sound pressure, we obtain an increase in the dB SPL level of about 6 dB SPL. Similarly, for a twofold reduction in the measured value, the dB SPL level will drop by 6 dB SPL. 

Using decibels is much more convenient than operating on pressure values, as the pressures considered usually fluctuate in the range from 20 μPa to even 2 Pa (0 dB SPL – 100 dB SPL). This is a difference of as much as 100 thousand.

It is also good to keep in mind that the pain threshold for the human ear ranges between 120 – 140 dB SPL.