The difference between a 100Hz frequency and a 200Hz frequency is perceived to be the same as the difference between a 1000Hz frequency and a 2000Hz frequency both intervals are considered to be one octave. On the logarithmic scale, to get from one of the large hash marks to the next, you need to multiply or divide by 10.įor example, humans perceive the pitch of a musical note on a logarithmic scale. This is clear on the scales above: on the linear scale, to get from one of the large hash marks to the next, you need to add or subtract by 10.

This is because linear scales compare additively, whereas logarithmic scales compare by multiplication. On the logarithmic scale, the distance between 1 and 10 is the same as the distance between 10 and 100. Note that on the linear scale, the distance from 0 to 10 is the same as the distance from 10 to 20. The image below shows a linear scale on top and a logarithmic scale on the bottom: Some quantities increase geometrically (1, 2, 4, 8, 16.) and combine by multiplication. In other words, the difference between 1 pascal (a unit of pressure) and 2 pascals is perceived as the same as the difference between 2 pascals and 4 pascals. However, not all quantities behave nicely like this. Most quantities that we're used to dealing with on a day-to-day basis increase arithmetically and combine additively, and therefore linear comparisons make sense for them. In other words, the difference between 1 meter and 2 meters is the same as the difference between 100 meters and 101 meters. Linear quantities like distance increase arithmetically (1, 2, 3, 4, 5.). For example, if the distance from point A to point B is 10 meters, and the distance from point B to point C is 100 meters, it makes sense to say that 'the total distance from A to B to C is 110 meters.' It also makes sense to say that 'the distance from B to C is 10 times further than A to B'. Measuring quantities on a linear scale makes sense for things that combine additively. For example, 'My car is 2 times faster than Jim's car', or 'my computer takes 3x longer to boot up than yours.' Note that the 'x' or 'times' unit is also not a unit of measurement it only compares two arbitrary values on a linear scale. The linear equivalent of the decibel unit is the 'x', or 'times' unit. We're used to comparing values on a linear scale, which is much more intuitive. But, this reinforces that decibels do not implicitly measure any physical quantity, they only compare two values on a logarithmic scale. Of course, these comparisons are somewhat nonsensical, and you'd never hear them used in a real scenario. 'Bill Gates has 59dB more money than I do.'.'It takes Bob 3dB more time to run a mile than it takes Jill.'.'The distance from New York to Tokyo is 5.9dB more than the distance from Chicago to Los Angeles.'.The following statements are perfectly valid: In contrast, decibels are simply a way of comparing two arbitrary values on a logarithmic scale.Įven though decibels are commonly used to measure sound levels, they can be used to compare any two values. Standard units of measurement (like meters, gallons, degrees Celsius, seconds) always measure physical quantities against a constant reference. The first thing to understand about decibels is that they are not units of measurement.

It is almost never used, as the deci-bel (1/10 of a Bel, since 'deci' is the SI prefix meaning 'one-tenth') is far more convenient. The official unit is the Bel, which is an order of magnitude or a power of ten, a single unit in the logarithmic number system. The unit they invented was initially called the Transmission Unit (TU) but was quickly renamed to the decibel (dB), in honor of telecommunications pioneer Alexander Graham Bell. This decibel unit allowed engineers to eliminate the previously-required complex calculations, and instead use simple addition. To simplify these calculations, Bell Telephone Labs invented the decibel for describing the magnitude of power loss. Predicting and measuring the performance and efficiency of these long-distance transmission lines involved complex calculations, especially when summing the power loss over multiple segments of long-distance transmission cables. In the late 19th and early 20th centuries, telegraph and telephone lines were quickly circling the globe. While decibels are most commonly thought of as describing sound volume, one might be surprised to learn that the origins of the decibel trace back to measuring electrical power loss over long-distance transmission cables.

Decibel scale examples rf