Definition of the concept

Almost everyone has heard of the decibel at least once in their life, but what actually is it? Let us try to clarify this. 

First and foremost, the decibel is a logarithmic and dimensionless unit. This simply means that it determines the measure of ratio values and requires a reference, because in itself it is not a unit of an absolute scale – such as a meter. Everyone knows exactly how much a meter is.

In the case of broadly understood acoustics, one very often encounters the decibel indicating the sound pressure level, i.e., dB SPL. Nevertheless, it should be mentioned that there are many different "types" of decibels – and each has its own unique application in physics.

Formula (dB SPL)

The decibel describing the sound pressure level (SPL) is given by the following formula:

where:

• p – measured sound pressure in Pa

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

The value of 20 μPa is the most common reference pressure for good reason. It is nothing other than the minimum sound pressure value that a human can "detect" with the hearing organ at a sound frequency of 1000 Hz. This is the threshold of hearing. The frequency was not chosen by chance; it is a value within the range where the human ear is most sensitive.

This formula leads to the statement that the level of 0 dB SPL is a sound pressure equal to the reference sound pressure, i.e., the threshold of hearing. Simple? Extremely so. 

The decibel as a logarithmic value

Since the decibel is not a linear but a logarithmic measure, it is worth noting that doubling the value of the measured sound pressure under no circumstances leads to doubling the decibel value. This naturally follows from the formula provided earlier. A simple example – let us assume a pressure of p1 = 200 μPa and p2 =  400 μPa. After substituting these into the formula, in the first case the dB SPL level will be 20 dB SPL, and in the second approximately 26 dB SPL. Thus, for a doubling of the measured sound pressure value, we obtain an increase in the dB SPL level of approximately 6 dB SPL. Analogously, for a twofold decrease in the measured value, the dB SPL level will drop by 6 dB SPL. In engineering practice, precise determination of noise levels in buildings requires laboratory equipment – check how we perform professional acoustic measurements for residential and commercial buildings.

Using decibels is much more convenient than working with pressure values, because the pressures under consideration typically range from 20 μPa to as much as 2 Pa (0 dB SPL – 100 dB SPL). This represents a difference of a factor of 100,000.

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