![]() ![]() 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.". ![]()
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