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What are Decibels? - Definition & Examples

Instructor: Thomas Zesiger

Thomas has taught electronics and communications engineering, math, and physics and has a master's degree in electrical engineering.

Have you ever heard of decibels? Do you ever wonder what they are and how they are used? This lesson explains what decibels are and provides examples of how they are used.

Definition

You may have heard of decibels, but may not be familiar with what they are and how they are used. To define a decibel, we break it down into two parts. The first part, 'deci-,' is a metric prefix that denotes a factor of one-tenth. Therefore, a decibel is one-tenth of a bel. The second part, '-bel,' is a unit of sound intensity that represents the ratio of sound pressure level. The unit is named after Alexander Graham Bell. The threshold of hearing is zero bel (10^-12 watts per square meter). Sound intensity is often measured in decibels and rarely in bels. The decibel unit is denoted by the abbreviation dB and is often referred to by people using it as 'dee-bees.'

The decibel has also found widespread use in electrical and electronics engineering to describe ratios of power, amplitude, voltage, temperature, frequency, and data rate. Although the dB is referred to as a unit, it is really a dimensionless quantity. Stated another way, it is a ratio of two quantities, rather than a unit. Mathematically, the units of the two quantities divide out, leaving it dimensionless. In these cases, the quantity is usually expressed as dB relative to another quantity. This is shown later in the lesson in several examples.

To give you some examples of how dB applies to sound, the sound levels to which we are routinely exposed to in everyday life range from zero dB to 120 dB. Sound levels over 85 dB are dangerous to hearing and levels above 120 dB can cause ear pain and permanent hearing loss. The graphic below shows the dB scale with some representative examples of sounds at each level.

Decibel scale showing levels of sounds encountered in everyday life.

Mathematical Expression

The bel scale, and consequently the decibel scale, is based on a logarithm with base ten. This means that it is based on factors of ten. For most applications involving the ratio of two quantities, say Q1 and Q2, bels are calculated by log base 10 (Q1/Q2). To express as decibels, we need to multiply this entire quantity by 10 due to the dB being one-tenth of a bel. When we do this, the expression becomes 10 * (log base 10 (Q1/Q2)). Some applications involve quantities that are squared. When inserted into our expression above, this becomes 10 * (log base 10 (Q1^2/Q2^2)). Using the rules of logarithms, this becomes 20 * (log base 10 (Q1/Q2)).

From these expressions, the dB scale is developed. A quantity of 10 dB is 10 times as intense as 0 dB. A quantity of 20 dB is 100, or 10^2 times, the intensity of zero dB. The scale follows this pattern so that, for example, a value of 80 dB is 100 times more intense than a 60-dB value. The table below shows the dB scale for power ratios used in electrical engineering.

Decibel power scale.

Power Example

Let's consider a power ratio of P1/P2, where P1 and P2 are separate power quantities. Using our expressions developed above, we have 10 * (log base 10 (P1/P2)). The abbreviation dB is often modified to indicate a reference level. For example, power may be expressed in dB relative to 1 watt (W). If we express 50 W in dB relative to 1 W, we have 10 * (log base 10 (50 W/1 W)) = 10 * (log base 10 (50)) = 10 * 1.7 = 17 dBW. This approach works for any set of power quantities or any other quantities that are not squared or raised to any other powers.

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