The threshold of hearing, 0dBSPL is a million times smaller in amplitude than 120dBSPL, commonly accepted as being the threshold of pain. Because of this, dealing with numbers using a linear scale isn’t convenient so a logarithmic scale is used which keeps things simpler.

Sound amplitude is referenced to the Pascal (Pa), the unit for measuring pressure.
0dBSPL = 0.00002 Pascals = 20 µPa
120dBSPL = 20 Pascals

*µ stands for micro

ch

The Decibel

The Bel is named after Alexander Graham Bell (1847 –1922), inventor of the telephone.
The decibel (dB) is a tenth of a Bel
In audio, amplitude is measured in decibels

The decibel (dB) is a logarithmic unit that expresses the ratio of one quantity relative to another quantity, e.g. 10 volts and 1000 volts. The decibel is typically used to measure quantities of power or intensity. The decibel is one tenth of a Bell. We use the decibel as it is a more appropriate resolution than the bell. For example 1dB is close to the JND (Just noticeable difference).

Our hearing works logarithmically (for both amplitude and pitch)

Logarithms are useful because we can conveniently represent very large or small numbers, and carry out multiplication of ratios by simple addition and subtraction

E.g.

1000 watts relative to 1 watt is 30dB
100,000 watts relative to 1 watt is 50dB
100,000,000 watts relative to 1 watt is 80d

The logarithm of a number is the power that the base has to be raised to produce that number.

The logarithm of 1000 is 3, because 1000 is 10 to the power 3
1000 = 10³ = 10 x 10 x 10

How to calculate a difference in dB:

The difference in dB between 10 and 1000

1000 / 10 = 100
Log100 = 2
Log100 = 2 Bells
2 Bells x 10 = 20 Decibels

2.1 The 0dB reference levels

0dBm = 0.001W
0dBu= 0.775V
0dBV = 1V
0dBSPL = 0.00002Pa

Formulas for dB equations are:

Sound Pressure Level
dBSPL = 20 x log (SPL / SPLref)

Voltage
dBV = 20 x log (V / Vref)
dBu = 20 x log (V / Vref)

Power (Watts)
dBm = 10 x log (P / Pref)

Power is the rate at which energy is produced or used

Sound Pressure Level is a logarithmic measure of the sound pressure relative to a reference level

Voltage is the potential difference between two points (e.g. the + and – sides of a battery). Voltage can be thought of as the pressure behind the electrons in a wire.

dBu is referenced to approximately 0.775 volts RMS (Root Mean Square)

Pro equipment signal level is +4dBu
Consumer equipment signal level is -10dBV
The level difference between +4dBu studio level and −10dBV consumer level is 12 dB

SPL and SIL

Sound Pressure Level (SPL) is measured in Pascals (Pa) and 0dBSPL is 0.00002Pa
Sound Intensity Level (SIL) is measured in watts per square meter (W/m2). 0dBSIL is: 10-12W/m2 or 0.000000000001W/m2

Sound Intensity (SIL) is difficult to measure that is why we typically use Sound Pressure (SPL).