What is decibel?; Simply explaining
They're a logarithmic unit that compares two magnitudes of the same phenomenon.
With them, you can compare things like voltage, current, power, gain, sound pressure, and more.
You might have seen in school but, as in earlier, you saw the number of logs, the log with specific bases of a positive real number is that number to raise the base in order to create that number.
The commonest logarithm would be base 10, like if one said, for example, that the logarithm of 100 is 2 because it could come from raising the power of 10 to the second power.
Logarithms, and so decibels, make things more amenable to comparison when you are dealing with great differences in the magnitude of the numbers, something one wouldn't want to use normally.
We can compare a reference with the computed decibel.
This kind of reference decibel gives the term its actual meaning.
They do not have units as they are a comparison of two equivalents, such as two sound pressure values or voltages, currents, etc., using decibels.
Using Decibels: A Matter of Perception
The way humans perceive things like sound pressure or light intensity isn’t linear.
A change that doubles the sound pressure in pascals isn’t perceived as double by our ears; instead, it follows a logarithmic scale.
In humans, changes in acoustic pressure and frequency are based on the percentage change from an initial condition, so they follow a mathematical scale.
It’s been proven that to increase the subjective level produced by a speaker, the applied power has to increase by 26% beyond the initial amount.
So, if we started with 1 Watt, we need to increase to 1.26 Watts to notice the change.
But if we started with 100 Watts, we’d need 126 Watts to get the same subjective increase.
That’s why logarithms are used to calculate decibels—they’re proportional numbers. In particular, base 10 is used for audio logarithm calculations.
Logarithmic Table
| Quantity | Logarithm (Bel) | 10 log (dB) |
|---|---|---|
| 1 | 0 | 0 |
| 10 | 1 | 10 |
| 100 | 2 | 20 |
| 1000 | 3 | 30 |
| 10000 | 4 | 40 |
In this table, logarithms serve two purposes: they act as a proportion and also compress the scale of values to make them easier to work with.
To calculate decibels (dB), we just multiply the Bel value by 10.
dB = 10 log (W1/W2)
This expression for calculating decibels applies to both electrical and acoustic power. If we want to calculate decibels for things other than power, like voltage or sound pressure, we need to make them proportional to power using the power equation.
Power Calculation Equation (in terms of voltage):
W = (V/R²)
Where:
- W is power in watts.
- V is voltage in volts.
- R is resistance in ohms.
With this in mind, and to simplify the operation, the square of the voltage is multiplied by the decibel expression. So, for calculating voltage and sound pressure, the decibel expression becomes:
dB = 20 log (V1/V2)
Referenced Decibels
In many applications of decibels, reference values of the studied magnitude are used to establish a meaningful point of comparison.
Decibels that use a comparative unit are called referenced decibels and can be identified by a suffix next to the "dB" term.
Depending on the phenomenon we’re studying (sound pressure, voltage, electrical power, etc.), we’ll use different references in each case.
The reference values come from a significant quantity for the phenomenon being studied.
| Type of Decibel | Name | Calculation | Reference |
|---|---|---|---|
| Acoustic Pressure | dB NPS | 20 log (P / Pref) | 20 x 10⁻⁶ Pascals |
| Voltage | dBV | 20 log (V / Vref) | 1 Volt |
| Voltage | dBu | 20 log (V / Vref) | 0.775 Volts |
| Electric Power | dBW | 10 log (W / Wref) | 1 Watt |
| Electric Power | dBm | 10 log (W / Wref) | 1x10⁻³ Watt |
dB NPS or dB SPL (Sound Pressure Level)
This is used when studying sound pressure and refers to how loud or perceived a source sounds.
The reference for calculating sound pressure level is the quietest sound a young, healthy person can hear at mid-range frequencies.
This is also known as the "threshold of hearing."
Sound pressure is measured in pascals, with a reference of 20 micropascals (20 x 10⁻⁶), which equals 0 dB. Keep in mind that since this is a pressure measurement, the expression for calculating decibels is:
dB NPS = 20 log (P / 20 x 10⁻⁶)
To get an idea of the range of hearing for the human ear, it goes from the reference value (20 micropascals) up to 200 pascals, which equals 140 dB.
The variation in sound pressure we perceive is immense (over a million times), which makes the decibel a great unit for compressing the scale and making comparisons easier.
Humans have such a wide hearing range as an evolutionary factor that helps us detect sounds that could represent danger.
| Hearing Threshold | Pressure (Pascals) | dB | Sound Type |
|---|---|---|---|
| Threshold of hearing | 20 x 10⁻⁶ | 0 | Soft sounds |
| Leaves rustling | 20 x 10⁻⁵ | 20 | Soft sounds |
| Quiet residence | 20 x 10⁻⁴ | 40 | Soft sounds |
| Normal conversation | 20 x 10⁻³ | 60 | Medium sounds |
| Noisy office or heavy traffic | 0.2 | 80 | Medium sounds |
| Heavy truck | 2 | 100 | Loud sounds |
| Running airplane engine | 20 | 120 | Loud sounds |
| Airplane takeoff | 200 | 140 | Threshold of pain |
Weighted Decibels
Weighted decibels include attenuation curves applied in sound pressure level measurement to better match what the ear perceives at different levels and frequencies.
The reason for using these curves is that the human ear doesn’t respond to all sound pressure levels the same way across frequencies.
Specifically, it has a pronounced filter for low and high frequencies at low listening levels.